Question 1

The average age of a class of 39 students is 15 years. If the age of the teacher is included, the average increases by 3 months. What is the age of the teacher in years?

Accepted Answer

Introduction / Context: This question tests your understanding of averages, especially when a new member is added to a group. The class has 39 students with a known average age, and when the teacher is added, the average increases slightly by 3 months. From this new average, you must compute the teacher age. This type of problem appears frequently in competitive exams because it requires comfortable handling of both averages and small unit conversions, such as months to years. Given Data / Assumptions: The class has 39 students with an average age of 15 years. When the teacher is added, the average age increases by 3 months. 3 months is one quarter of a year, that is 0.25 years. The new average age with the teacher included is therefore 15.25 years. We must find the teacher age. Concept / Approach: Average age is total age divided by number of individuals. First, calculate the total age of all 39 students. Then, calculate the total age for 40 individuals (39 students plus the teacher) using the new average. The difference between these two totals gives the teacher age. This approach is systematic and avoids confusion about how the additional person affects the average. Step-by-Step Solution: Step 1: Compute the total age of 39 students as 39 × 15 = 585 years. Step 2: When the teacher is included, the group becomes 40 individuals with an average age of 15.25 years. Step 3: Compute the total age of these 40 individuals as 40 × 15.25 = 610 years. Step 4: The teacher age is the difference between the total age with the teacher and the total age of the students alone, so teacher age = 610 − 585 = 25 years. Step 5: Thus, the teacher age is 25 years. Verification / Alternative check: Think in terms of the effect of the teacher age compared to the original average. The new average is higher by 0.25 years across 40 individuals, which means the total increase in age is 40 × 0.25 = 10 years. Therefore, the teacher must be 10 years older than the original average, so the teacher age is 15 + 10 = 25 years. This matches the previous calculation using totals and confirms that the answer is correct. Why Other Options Are Wrong: Option 30: This would produce a larger increase in total age than necessary and result in an average more than 15.25 years. Option 35 and 40: These values are much higher than required to increase the average by only 3 months and would give a larger jump in the group average. Option 28: Although closer, it still yields a larger total than the allowed 610 years and does not correspond to the given new average. Common Pitfalls: A frequent mistake is to treat 3 months as 3 years or 0.3 years, which leads to incorrect totals. Another error is to forget that the number of individuals changes from 39 to 40 when the teacher is added. Always convert months to years correctly and remember that total age equals average multiplied by number of people. Verifying the result by checking the implied average is a good way to catch mistakes. Final Answer: The age of the teacher is 25 years.

Question 2

K is 5 years older than H. H is 3 years younger than R. R is 6 years older than C. C is 7 years younger than L. Based on this chain of age relations, who is the eldest among K, H, R, C and L?

Accepted Answer

Introduction / Context: This is a logical age comparison question involving several people connected by a chain of older and younger relationships. Instead of requiring algebraic equations, it mainly tests your ability to interpret and combine relative age statements correctly. Such questions often appear in reasoning sections of aptitude tests to check clarity of thought and careful reading. Given Data / Assumptions: K is 5 years older than H. H is 3 years younger than R. R is 6 years older than C. C is 7 years younger than L. We need to determine who is the eldest among K, H, R, C and L. Concept / Approach: The approach is to pick one person as a reference and express all other ages relative to that person using differences. It is convenient to choose C as the reference because several statements connect to C through R and L. Once the ages of R, H, K and L are written in terms of C, we can compare the expressions to see who has the largest value, and therefore who is the eldest. This process uses only basic arithmetic with plus and minus signs. Step-by-Step Solution: Step 1: Let the present age of C be c years. Step 2: R is 6 years older than C, so R age is c + 6. Step 3: H is 3 years younger than R, so H age is (c + 6) − 3 = c + 3. Step 4: K is 5 years older than H, so K age is (c + 3) + 5 = c + 8. Step 5: C is 7 years younger than L, so L age is c + 7. Step 6: Compare all expressions: C has c, H has c + 3, R has c + 6, L has c + 7, and K has c + 8. The largest among these is c + 8, so K is the eldest. Verification / Alternative check: To visualize, assign any convenient value to c, for example c = 10 years. Then R = 16, H = 13, K = 18 and L = 17. In this illustrative scenario, K is 18 years old, which is older than everyone else. Because only constant differences were used to relate ages to c, the relative ordering does not change if we choose a different value for c. Therefore, K is always the eldest regardless of the specific value of c, as long as all relations hold. Why Other Options Are Wrong: Option H: H age is c + 3, which is less than c + 8, so H cannot be the eldest. Option R: R age is c + 6, still smaller than c + 8. Option L: L age is c + 7, closer to K age but still one year younger than K. Option C: C age is c, the smallest of all expressed ages, so C is definitely not the eldest. Common Pitfalls: A common mistake is to misread younger than and older than and reverse the sign when forming expressions. Another error is to try to assign actual numbers without maintaining the given differences properly, which can lead to an incorrect ordering. A reliable strategy is to choose a reference person, write everyone else age in terms of that reference, and then compare the resulting expressions directly. This ensures that relative age comparisons remain clear and consistent. Final Answer: The eldest among the five people is K.

Question 3

In a quantitative aptitude problem on ages, the present age of Dr Pandey is four times the present age of his son. After 10 years, the age of Dr Pandey will be exactly twice the age of his son at that time. What is the present age, in years, of the …

Accepted Answer

Introduction / Context: This is a standard aptitude question on ages where present ages are connected to future ages using simple linear relationships. Such problems test whether you can convert English statements like “four times” and “twice the age after 10 years” into algebraic equations, and then solve them correctly. Mastering this pattern is very useful for bank exams, SSC exams and other quantitative reasoning tests. Given Data / Assumptions: The present age of Dr Pandey is four times the present age of his son. After 10 years, the age of Dr Pandey will be exactly twice the age of his son at that time. We are asked to find the present age of the son in years. All ages are measured in whole years and are positive. Concept / Approach: The idea is to assume a variable for the unknown present age of the son and then write expressions for present and future ages. Phrases like “four times” translate to multiplication by 4, and “after 10 years” means we add 10 to the present age. The statement that one age becomes “twice” another age after a fixed time becomes an equation which we can solve using basic algebra. Once the value of the variable is obtained, we interpret it as the required present age of the son. Step-by-Step Solution: Step 1: Let the present age of the son be x years. Step 2: Then the present age of Dr Pandey is 4x years, because it is four times the age of his son. Step 3: After 10 years, the son will be x + 10 years old. Step 4: After 10 years, Dr Pandey will be 4x + 10 years old. Step 5: According to the question, after 10 years the age of Dr Pandey will be twice the age of his son, so we form the equation 4x + 10 = 2 * (x + 10). Step 6: Expand the right side: 4x + 10 = 2x + 20. Step 7: Rearrange to bring variables to one side: 4x - 2x = 20 - 10, so 2x = 10. Step 8: Divide by 2 to get x = 5. Step 9: Therefore the present age of the son is 5 years. Verification / Alternative check: We can quickly verify the result by substituting back into the story. If the son is 5 years old now, Dr Pandey is 4 * 5 = 20 years old. After 10 years, the son will be 5 + 10 = 15 years old and Dr Pandey will be 20 + 10 = 30 years old. At that time, 30 is exactly twice 15, which perfectly matches the condition in the question, so the solution is consistent. Why Other Options Are Wrong: Option A (4 years) would make the father 16 years old now and 26 after 10 years, while the son would be 14 after 10 years. Then 26 is not twice 14, so this is incorrect. Option C (6 years) would give present ages 6 and 24. After 10 years, they become 16 and 34, and 34 is not twice 16, so this option fails. Option D (8 years) would give present ages 8 and 32. After 10 years, the ages would be 18 and 42, and 42 is not twice 18, so this is also wrong. Common Pitfalls: A common mistake is to confuse present ages with future ages and directly apply the “twice” relation on present ages. Another frequent error is to forget that both father and son age by the same number of years, in this case 10 years. Carefully translating each line of the statement into algebra avoids these mistakes. Final Answer: The correct present age of the son of Dr Pandey is 5 years.

Question 4

Three years ago, the average age of a family of five members was 17 years. A new baby was born after that, and today the average age of the family remains the same as before. What is the present age, in years, of the baby?

Accepted Answer

Introduction / Context: This question is about averages and ages in a family before and after the birth of a child. Such problems commonly appear in aptitude tests because they combine the concept of average with changes in group size. Understanding how the total sum of ages changes while the average may remain constant is essential for solving these questions quickly and correctly. Given Data / Assumptions: Three years ago, there were 5 family members and their average age was 17 years. After that, a baby was born, so now there are 6 family members. The current average age of the 6 members is still 17 years. We must find the present age of the baby in years. All ages are measured in years and are non negative. Concept / Approach: Average age is defined as total sum of ages divided by the number of people. When we know the average, we can easily compute the total sum. Over time, ages of existing members increase, which changes the total sum even if the average remains the same. By writing expressions for total ages three years ago and today, and then comparing them, we can isolate the contribution of the baby and calculate the baby age. Step-by-Step Solution: Step 1: Three years ago, there were 5 members with an average age of 17 years, so the total age then was 5 * 17 = 85 years. Step 2: In the next three years, each of those 5 members became 3 years older, adding 3 * 5 = 15 years to the total. Step 3: Therefore, the total age of the original 5 members today is 85 + 15 = 100 years. Step 4: Now there are 6 members (including the baby) and the current average age is still 17 years. Step 5: So the total age of all 6 members today is 6 * 17 = 102 years. Step 6: The total age contributed by the baby today is 102 - 100 = 2 years. Step 7: Therefore the present age of the baby is 2 years. Verification / Alternative check: To verify, distribute the total ages. The 5 original members currently have 100 years combined, and the baby has 2 years, so the total is 102 years. Dividing 102 by 6 gives 17, matching the stated average. This confirms that 2 years is the correct age for the baby. No contradictions arise from this value, so the solution is sound. Why Other Options Are Wrong: Option B (2.4 years) would mean the total age of all 6 members is 100 + 2.4 = 102.4 years, which does not give an average of exactly 17 years. Option C (3 years) would make the total 103 years, giving an average of 103 / 6 which is greater than 17, so it is wrong. Option D (1.5 years) would give a total of 101.5 years and again the average would not be exactly 17 years, so this option is incorrect. Common Pitfalls: Students often forget to increase the ages of the original members over the three year period, or they directly assume the baby age is 3 years because three years have passed. It is also common to confuse the number of family members at different times. Always compute totals step by step and pay close attention to how many members are present at each moment. Final Answer: The present age of the baby is 2 years.

Question 5

When their son was born, the ratio of the ages of a father and a mother was 11 : 10. When the son becomes twice his present age in the future, the ratio of the ages of the father and the mother will be 19 : 18. What is the ratio of the present ages …

Accepted Answer

Introduction / Context: This problem involves ratios of ages at different points in time and an indirect role of the son age. It is a classic example of how age ratio questions use past and future information together. The goal is to convert the given ratio statements into equations and eliminate the son age to get a direct ratio between the present ages of the father and the mother. Given Data / Assumptions: When the son was born, the ratio of the ages of the father and mother was 11 : 10. In the future, when the son becomes twice his present age, the ratio of the ages of the father and mother will be 19 : 18. We must find the ratio of the present ages of the father and the mother. Ages are measured in years and assumed to be positive. Concept / Approach: The key idea is to introduce variables for present ages and relate them to ages at different times. At the time of birth of the son, both parents were younger by an amount equal to the son current age. At the future time when the son doubles his age, both parents are older by the same number of years. Both conditions are expressed as ratios that can be converted into algebraic equations. Solving these equations simultaneously allows us to determine the ratio of present ages of the parents without needing their exact ages. Step-by-Step Solution: Step 1: Let the present age of the father be F years and the present age of the mother be M years. Let the present age of the son be S years. Step 2: At the time of the son birth, the son age was 0 and both parents were younger by S years, so their ages were F - S and M - S. Step 3: At that time, (F - S) : (M - S) = 11 : 10. Step 4: This gives the equation (F - S) / (M - S) = 11 / 10. Step 5: In the future, when the son is twice his present age, his age will be 2S. To reach that age from S, a time interval of S years must pass. Step 6: After S years, the father age will be F + S and the mother age will be M + S. Step 7: At that time, (F + S) : (M + S) = 19 : 18, so (F + S) / (M + S) = 19 / 18. Step 8: From the first ratio, write F - S = 11k and M - S = 10k for some positive constant k. Step 9: From the second ratio, write F + S = 19t and M + S = 18t for some constant t. Step 10: Solving these equations gives F = 15t and M = 14t, which means the present age ratio F : M is 15 : 14. Verification / Alternative check: To verify, assume t = 1 for simplicity. Then F = 15 and M = 14. The son present age from the equations would be S = 4. At birth, the father and mother would be 11 and 10 respectively, giving the required ratio 11 : 10. After 4 years, when the son is 8 years old, the father and mother would be 19 and 18 respectively, giving the second ratio 19 : 18. Both conditions match perfectly, so the ratio 15 : 14 is correct. Why Other Options Are Wrong: Option B (14 : 13) cannot satisfy both sets of ratio conditions when tested in a similar way, so it is invalid. Option C (16 : 15) also fails when substituted into the past and future relationships, leading to contradictions. Option D (17 : 16) similarly does not produce the specified ratios of 11 : 10 and 19 : 18 at the required times. Common Pitfalls: A frequent error is to treat ratios as if they directly compare present ages without accounting for the changes over time. Another pitfall is to assume a fixed difference that does not respect the given ratios. The safe method is to introduce variables and constants for ratios, write equations carefully and then solve systematically. Working with symbolic constants like k and t helps keep the algebra manageable. Final Answer: The ratio of the present ages of the father and the mother is 15 : 14.

Question 6

The present ages of Rangana and Sayed are in the ratio 7 : 5. After 11 years, the ratio of their ages will become 4 : 3. What is the present age, in years, of Rangana?

Accepted Answer

Introduction / Context: This question is a typical example of age ratio problems where the ratio of ages is given at the present time and at a future time. Such problems are designed to check your ability to translate ratios and time shifts into linear equations and then solve for actual ages. This pattern appears frequently in aptitude exams because it combines proportional reasoning with basic algebra. Given Data / Assumptions: The present age ratio of Rangana and Sayed is 7 : 5. After 11 years, the ratio of their ages will become 4 : 3. We must find the present age of Rangana in years. All ages are expressed in years and are positive integers. Concept / Approach: When ages are given in ratio form, we can represent them as multiples of a common variable. Time shifts such as “after 11 years” are handled by adding 11 to each person age expression. Setting the future ratio equal to the given fraction produces an equation in the common variable. Solving that equation gives the actual ages. This method avoids guesswork and ensures a systematic solution. Step-by-Step Solution: Step 1: Let the present age of Rangana be 7x years and the present age of Sayed be 5x years, where x is a positive constant. Step 2: After 11 years, Rangana age will be 7x + 11 years. Step 3: After 11 years, Sayed age will be 5x + 11 years. Step 4: At that time the ratio of their ages is given as 4 : 3, so (7x + 11) / (5x + 11) = 4 / 3. Step 5: Cross multiply to clear the fraction: 3 * (7x + 11) = 4 * (5x + 11). Step 6: Expand both sides: 21x + 33 = 20x + 44. Step 7: Rearrange terms: 21x - 20x = 44 - 33, so x = 11. Step 8: Substitute back to find Rangana present age: 7x = 7 * 11 = 77 years. Step 9: Therefore, the present age of Rangana is 77 years. Verification / Alternative check: Check the result by computing future ages. If x = 11, Sayed present age is 5 * 11 = 55 years. After 11 years, Rangana will be 77 + 11 = 88 years and Sayed will be 55 + 11 = 66 years. The ratio 88 : 66 simplifies by dividing both numbers by 22 to give 4 : 3, exactly matching the condition in the question. Hence the answer is verified as correct. Why Other Options Are Wrong: Option A (55 years) would make Sayed age too small compared to the required ratio, and the future ratio would not turn into 4 : 3. Option C (70 years) does not satisfy the future ratio when combined with a consistent age for Sayed, so it is not valid. Option D (96 years) leads to a future ratio that deviates significantly from 4 : 3, so this option is also incorrect. Common Pitfalls: Learners sometimes incorrectly add 11 only to one age in the ratio instead of to both. Another mistake is to treat the ratio values as direct ages without introducing a variable multiple. Always represent ratio based ages as multiples of a common variable and then apply the time shift to all people involved. Cross multiplying carefully avoids algebraic errors and leads to a clean solution. Final Answer: The present age of Rangana is 77 years.

Question 7

The ratio of the present ages of Rahul and his sister is 3 : 4. Ten years ago, the ratio of their ages was 13 : 19. What is the present age, in years, of Rahul?

Accepted Answer

Introduction / Context: This question involves comparing age ratios at the present time and in the past. It is a typical problem in the topic of ages where simple algebra and careful interpretation of ratios are required. By converting each ratio statement into an equation involving a common variable and then using the time shift of ten years, we can determine the actual present age of Rahul. Given Data / Assumptions: The present age ratio of Rahul and his sister is 3 : 4. Ten years ago, the ratio of their ages was 13 : 19. We are asked to find the present age of Rahul in years. All ages are positive and measured in years. Concept / Approach: When ages are given in ratio form, we model them as multiples of a common factor. Since there is a time difference of ten years, we subtract ten from each present age expression to get past ages. We then set the fraction of past ages equal to the given past ratio. This yields a single equation in one variable, which can be solved to get the common multiple and thus the actual age of Rahul. Step-by-Step Solution: Step 1: Let the present age of Rahul be 3x years and the present age of his sister be 4x years. Step 2: Ten years ago, Rahul age would have been 3x - 10 years. Step 3: Ten years ago, his sister age would have been 4x - 10 years. Step 4: At that time, the ratio of their ages is given as 13 : 19, so (3x - 10) / (4x - 10) = 13 / 19. Step 5: Cross multiply to get 19 * (3x - 10) = 13 * (4x - 10). Step 6: Expand both sides: 57x - 190 = 52x - 130. Step 7: Rearrange terms: 57x - 52x = -130 + 190, so 5x = 60. Step 8: Divide by 5 to get x = 12. Step 9: Therefore, Rahul present age is 3x = 3 * 12 = 36 years. Verification / Alternative check: Check the ages ten years ago. Rahul would be 36 - 10 = 26 years, and his sister would be 4 * 12 - 10 = 48 - 10 = 38 years. The ratio 26 : 38 can be simplified by dividing both numbers by 2 to get 13 : 19, which exactly matches the given past ratio. This confirms that our calculation is correct and that Rahul present age is indeed 36 years. Why Other Options Are Wrong: Option B (48 years) would produce a different past ratio that does not simplify to 13 : 19 when paired with the corresponding age of his sister. Option C (42 years) similarly fails to produce the required past ratio and therefore is incorrect. Option D (54 years) leads to past ages that do not satisfy the ratio 13 : 19, making this option invalid as well. Common Pitfalls: One common mistake is to add or subtract the time difference from only one of the ages, but both individuals age equally over time. Another pitfall is to treat ratios as simple differences instead of fractional relationships, which causes errors in forming the equations. Always write the ratio as a fraction and then cross multiply carefully to avoid algebraic mistakes. Final Answer: The present age of Rahul is 36 years.

Question 8

Amit age is four times the age of Babli, and Babli age is three times the age of Priya. If the present age of Priya is 5 years, what is the present age, in years, of Amit?

Accepted Answer

Introduction / Context: This question is a straightforward chain ratio problem about ages. It involves three people whose ages are related by simple multiplication factors. Such questions test your ability to follow one relation after another and apply proportional thinking. They do not require forming complex equations and are therefore common in the easier section of quantitative aptitude tests. Given Data / Assumptions: Amit present age is four times the age of Babli. Babli present age is three times the age of Priya. Priya present age is given as 5 years. We need to find the present age of Amit in years. All ages are in years and are non negative. Concept / Approach: The approach is to start from the known age and move step by step through the chain of relationships. First, we use Priya age to compute Babli age, then we use Babli age to compute Amit age. Since each relation is expressed as a multiple, no equations or ratios are needed beyond simple multiplication. This reflects the concept of compound proportionality where one quantity depends on another which itself depends on a third quantity. Step-by-Step Solution: Step 1: Priya present age is given as 5 years. Step 2: Babli present age is three times the age of Priya, so Babli age is 3 * 5 = 15 years. Step 3: Amit present age is four times the age of Babli. Step 4: Therefore Amit age is 4 * 15 = 60 years. Step 5: We conclude that Amit is 60 years old at present. Verification / Alternative check: We can verify by tracing the chain backwards. If Amit is 60 years old, then Babli should be 60 / 4 = 15 years old, which matches our value of 15. If Babli is 15 years old, Priya should be 15 / 3 = 5 years old, which is exactly the given age of Priya. Since both directions of the chain are consistent, the calculation is correct. Why Other Options Are Wrong: Option A (65 years) would imply Babli age is 65 / 4, which is not a whole number and does not match the given multiple of 3 times Priya age, so it is invalid. Option B (45 years) would yield Babli age as 45 / 4 which again is inconsistent with an integer multiple of 5 years for Priya, so it is incorrect. Option C (55 years) similarly fails to maintain the exact 4 times and 3 times relationships when traced through Babli and Priya ages. Common Pitfalls: A common error is to mix up the direction of the relationships, for example taking Priya to be three times Babli instead of Babli being three times Priya. Another mistake is to perform addition instead of multiplication when the statement clearly indicates a multiple. Reading the statements slowly and identifying the correct multiplication factors for each step helps avoid such confusion. Final Answer: The present age of Amit is 60 years.

Question 9

The total of the present ages of Ashok, Akbar and Anil is 65 years. What was the total of their ages six years ago?

Accepted Answer

Introduction / Context: This question belongs to the basic level of age problems where the total present age of a group is known and we are asked to find the total at some time in the past. It tests whether you understand that each person age changes by the same amount over a fixed time period, and hence the total change in the sum of ages is simply the number of people multiplied by that time interval. Given Data / Assumptions: The total of the present ages of Ashok, Akbar and Anil is 65 years. We have to find the total of their ages six years ago. There are exactly three people in the group. All ages are measured in years. Concept / Approach: If there are n people in a group, then going back t years means each person age is reduced by t years. Therefore, the sum of their ages t years ago is the present sum minus n * t. This applies regardless of how old each individual is, as long as the number of people remains the same. Here, n is 3 and t is 6, so we can compute the total six years ago directly from the given total present age. Step-by-Step Solution: Step 1: The present total age of Ashok, Akbar and Anil is given as 65 years. Step 2: Six years ago, each of the three people was 6 years younger than they are now. Step 3: The total decrease in the sum of ages over 6 years for 3 people is 3 * 6 = 18 years. Step 4: Therefore, the sum of their ages six years ago was 65 - 18 years. Step 5: Compute the difference: 65 - 18 = 47 years. Step 6: So, the total of their ages six years ago was 47 years. Verification / Alternative check: As an alternative check, imagine any three ages that now add up to 65 years, for example 20, 22 and 23. Six years ago these would have been 14, 16 and 17, and their sum would be 47. This shows that regardless of the individual distribution, the total decreases by 18 years, confirming the formula and result. The key is that only the total matters for this question. Why Other Options Are Wrong: Option A (59 years) represents a decrease of only 6 years, which would correspond to only one person getting younger, not three people, so it is incorrect. Option B (43 years) would imply a decrease of 22 years, which does not match 3 * 6 and therefore is not possible for three people going back six years. Option C (57 years) corresponds to a decrease of 8 years, again not equal to 18 years, so it is also wrong. Common Pitfalls: Many learners mistakenly subtract 6 only once from the total instead of six times for each of the three people. Others attempt to guess individual ages even though they are not needed. Remember that when the number of people is fixed, total change over t years for n people is n * t, which simplifies such problems greatly. Final Answer: The total of their ages six years ago was 47 years.

Question 10

The present ages of Sohail, Afzal and Bilal are 17 years, 16 years and 12 years respectively. If the age of Aslam is also included, the average age of the group increases by 5 years. What is the present age, in years, of Aslam?

Accepted Answer

Introduction / Context: This problem is about how the average age of a group changes when a new member is added. It is common in quantitative aptitude sections dealing with averages and age based questions. The key point is to understand how total age and number of persons interact to produce the average, and how to reverse engineer the unknown age of a newly added person from the change in average. Given Data / Assumptions: Present ages are 17 years for Sohail, 16 years for Afzal and 12 years for Bilal. When Aslam age is included, the average age of the group increases by 5 years compared to the average of the first three. We must find the present age of Aslam. All ages are in years and considered positive. Concept / Approach: First, we compute the average age of the initial three people. Then, using the given information that the new average with four people is 5 years more, we compute the new average. Multiplying each average by the number of people gives the total of their ages. The difference between the total for four people and the total for three people must be the age of Aslam. This is a standard application of the formula average = total sum divided by number of items. Step-by-Step Solution: Step 1: Compute the total age of Sohail, Afzal and Bilal: 17 + 16 + 12 = 45 years. Step 2: Find the average age of these three individuals: 45 / 3 = 15 years. Step 3: When Aslam is included, the average age increases by 5 years, so the new average becomes 15 + 5 = 20 years. Step 4: With Aslam added, there are now 4 people in the group. Step 5: The total age of all four people is new average * number of people = 20 * 4 = 80 years. Step 6: The total age of the first three was 45 years, so the age of Aslam is 80 - 45 = 35 years. Step 7: Therefore, Aslam present age is 35 years. Verification / Alternative check: We can verify by checking the average with the calculated age. If Aslam is 35 years old, the four ages are 17, 16, 12 and 35. Their sum is 17 + 16 + 12 + 35 = 80 years. The average is 80 / 4 = 20 years. This is exactly 5 years more than the original average of 15 years that we calculated for the first three. The conditions are satisfied, confirming that 35 years is the correct age for Aslam. Why Other Options Are Wrong: Option A (32 years) would produce a total of 45 + 32 = 77 years, giving an average of 77 / 4 which is less than 20, so the increase of 5 years would not hold. Option B (33 years) leads to a total of 78 and an average of 19.5 years, again not an increase of exactly 5 years. Option C (34 years) gives a total of 79 years, with an average of 19.75 years, which still does not match the required new average of 20 years. Common Pitfalls: Students sometimes mistakenly add 5 years to each individual age instead of interpreting it as a change in the average. Another common mistake is to forget to multiply the average by the correct number of people when reconstructing the total. Always remember that the total sum is the average multiplied by the number of items, and small arithmetic errors in this step can lead to wrong answers. Final Answer: The present age of Aslam is 35 years.

Question 11

The ratio of the present ages of Raman and Lamba is 7 : 5. After 6 years, the age of Raman will be 48 years. What is the present age, in years, of Lamba?

Accepted Answer

Introduction / Context: This is a simple age ratio problem where the future age of one person is given explicitly, and the present age ratio between two people is also provided. Such problems are common in aptitude tests because they can be solved straightforwardly using proportional reasoning and basic arithmetic, without lengthy algebra. Given Data / Assumptions: The present age ratio of Raman and Lamba is 7 : 5. After 6 years, Raman age will be 48 years. We must determine the present age of Lamba. All ages are given in years and are positive. Concept / Approach: We model present ages in terms of a common multiple. If Raman present age is 7k and Lamba present age is 5k, then after 6 years Raman will be 7k + 6. Since this is told to be 48 years, we can solve for k directly. Once k is known, we substitute into 5k to find Lamba present age. This technique of representing ages based on ratios is standard for such problems. Step-by-Step Solution: Step 1: Let the present age of Raman be 7k years and the present age of Lamba be 5k years. Step 2: After 6 years, Raman age will be 7k + 6 years. Step 3: According to the question, after 6 years Raman age is 48 years, so 7k + 6 = 48. Step 4: Subtract 6 from both sides to get 7k = 42. Step 5: Divide by 7 to find k = 6. Step 6: Lamba present age is 5k years, so it is 5 * 6 = 30 years. Step 7: Therefore the present age of Lamba is 30 years. Verification / Alternative check: With k = 6, Raman present age is 7 * 6 = 42 years. After 6 years, Raman will be 42 + 6 = 48 years, which matches the condition given in the question. Lamba present age is 30 years, and their present ratio is 42 : 30 which simplifies to 7 : 5 by dividing both numbers by 6. Thus, both the ratio and the future age condition are satisfied, confirming the correctness of the answer. Why Other Options Are Wrong: Option B (25 years) would give a present ratio that does not simplify cleanly to 7 : 5 when paired with Raman correct present age, so it is wrong. Option C (35 years) would make Lamba too old relative to Raman, and the ratio 42 : 35 does not equal 7 : 5. Option D (40 years) clearly does not fit the ratio 7 : 5 with Raman present age of 42 years, so it is also incorrect. Common Pitfalls: Learners may mistakenly assume that the ratio applies to future ages rather than present ages, which leads to incorrect equations. Another error is to try to guess ages without using a variable, which can be time consuming and unreliable. Always express ratio based ages as multiples of a variable and use the given future or past condition to solve systematically. Final Answer: The present age of Lamba is 30 years.

Question 12

The ratio of the present ages of P and Q is 8 : 5. After 4 years, their ages will be in the ratio 4 : 3 respectively. What will be the ratio of the age of P after 7 years from now to the present age of Q?

Accepted Answer

Introduction / Context: This question combines present and future age ratios of two people and then asks for a different ratio involving another time shift. It is a good test of your ability to manage multiple time based changes and ratios using algebra. Problems like this are common in competitive exams where ratio and proportion and age based reasoning are tested together. Given Data / Assumptions: The present age ratio of P and Q is 8 : 5. After 4 years, their ages will be in the ratio 4 : 3. We are asked for the ratio of P age after 7 years from now to the present age of Q. All ages are in years and positive. Concept / Approach: First, we express the present ages in terms of a common multiple. Then we use the future ratio after 4 years to form an equation and solve for the common multiple. Once the actual present ages of P and Q are known, we can compute P age after 7 years and then form the requested ratio with Q present age. The problem demonstrates how time shifts can be handled systematically with simple algebra. Step-by-Step Solution: Step 1: Let the present age of P be 8x years and the present age of Q be 5x years. Step 2: After 4 years, P age will be 8x + 4 years and Q age will be 5x + 4 years. Step 3: At that time, the ratio of their ages is given as 4 : 3, so (8x + 4) / (5x + 4) = 4 / 3. Step 4: Cross multiply to obtain 3 * (8x + 4) = 4 * (5x + 4). Step 5: Expand both sides: 24x + 12 = 20x + 16. Step 6: Rearrange the equation: 24x - 20x = 16 - 12, so 4x = 4. Step 7: Divide both sides by 4 to get x = 1. Step 8: Therefore, present ages are P = 8 * 1 = 8 years and Q = 5 * 1 = 5 years. Step 9: P age after 7 years will be 8 + 7 = 15 years. Step 10: We need the ratio of P age after 7 years to Q present age, that is 15 : 5. Step 11: Simplify 15 : 5 by dividing both terms by 5 to get 3 : 1. Verification / Alternative check: As a quick check, verify the given after 4 years ratio. After 4 years, P will be 8 + 4 = 12 years and Q will be 5 + 4 = 9 years. The ratio 12 : 9 simplifies to 4 : 3, which matches the problem statement. Next, P age after 7 years is 15 years and Q present age is 5 years, so the ratio 15 : 5 simplifies correctly to 3 : 1. Therefore, the solution is consistent. Why Other Options Are Wrong: Option A (3 : 2) would imply that P after 7 years is only 1.5 times Q present age, which contradicts the calculated values of 15 and 5. Option B (1 : 2) suggests that P would be younger or much smaller in comparison to Q, which is inconsistent with the determined ages. Option C (2 : 1) does not match the exact ratio of 15 : 5, which simplifies to 3 : 1, not 2 : 1. Common Pitfalls: Students sometimes confuse which ages are used in the final ratio and may incorrectly use Q age after 7 years instead of Q present age. Another common mistake is to forget to add the correct number of years to both ages when forming the future ratio. Careful reading of the question and clear labeling of each age expression helps avoid such errors. Final Answer: The required ratio is 3 : 1.

Question 13

The average age of Hari, his wife and their two children is 23 years. His wife is 4 years younger than Hari. She was 20 years old when their daughter was born, and Hari was 28 years old when their son was born. What is the sum of the present ages, i…

Accepted Answer

Introduction / Context: This problem combines average age concepts with age differences between family members and information about how old the parents were when their children were born. It is a classic mixed age problem seen in aptitude tests that checks your ability to set up equations from several related statements and derive the required sum of ages. Given Data / Assumptions: The family consists of Hari, his wife, their daughter and their son, four people in total. The average age of these four family members is 23 years. Hari wife is 4 years younger than Hari. Hari wife was 20 years old when their daughter was born. Hari was 28 years old when their son was born. We need the sum of the present ages of Hari and his daughter. Concept / Approach: First, we use the average age to get the total of all four present ages. Next, we represent Hari age as a variable and use the information about age differences and birth times to express the ages of his wife, daughter and son in terms of the same variable. This leads to one equation in one unknown, which we solve to get Hari present age. Then we find the daughter present age and add it to Hari age to obtain the required sum. Step-by-Step Solution: Step 1: Let Hari present age be H years. Step 2: His wife is 4 years younger, so her present age is H - 4 years. Step 3: She was 20 years old when their daughter was born, so the daughter present age is (H - 4) - 20 = H - 24 years. Step 4: Hari was 28 years old when their son was born, so the son present age is H - 28 years. Step 5: The family has four members and their average age is 23 years, so the total of their present ages is 4 * 23 = 92 years. Step 6: The sum of their present ages in terms of H is H + (H - 4) + (H - 24) + (H - 28) = 4H - 56. Step 7: Set this equal to 92: 4H - 56 = 92. Step 8: Add 56 to both sides to get 4H = 148. Step 9: Divide both sides by 4 to obtain H = 37. Step 10: Therefore, Hari present age is 37 years and the daughter present age is H - 24 = 37 - 24 = 13 years. Step 11: The sum of the present ages of Hari and his daughter is 37 + 13 = 50 years. Verification / Alternative check: Let us verify by computing all four ages. Hari is 37 years old, his wife is 37 - 4 = 33 years old, their daughter is 13 years old and their son is 37 - 28 = 9 years old. The total of the four ages is 37 + 33 + 13 + 9 = 92 years. Dividing by 4 gives an average of 92 / 4 = 23 years, which matches the given average. The ages are also consistent with the birth information, confirming that our calculation is correct. Why Other Options Are Wrong: Option A (53 years) does not match the sum 37 + 13 and would require different ages which would break the given average or birth conditions. Option B (55 years) similarly does not correspond to any consistent set of ages satisfying all the given statements. Option C (56 years) is also inconsistent with the required average age and age differences among family members. Common Pitfalls: Students may misinterpret statements like “she was 20 years old when their daughter was born” and incorrectly add or subtract years. Another common mistake is to forget that the average applies to the total of all four members. Using a clear variable for Hari age and writing each family member age in terms of this variable prevents such errors and leads to a systematic solution. Final Answer: The sum of the present ages of Hari and his daughter is 50 years.

Question 14

If 6 years are subtracted from the present age of Ayush and 25 percent of the remaining value is taken, we get the present age of his only son. Four years ago, the present age of his daughter was 7 years more than the age of his son at that time. Th…

Accepted Answer

Introduction / Context: This is a multi step age problem involving four members of a family: Ayush, his wife, his son and his daughter. It combines percentages, average age, and age relations at different times. Such questions are considered challenging in aptitude exams because they require setting up several equations from a dense verbal description and solving them logically without losing track of the relationships. Given Data / Assumptions: Let Ayush present age be A years. If 6 years are subtracted from A and 25 percent of the result is taken, that value equals the present age of his son. Four years ago, the daughter age was 7 years more than the son age at that time. The sum of the present ages of the daughter and Ayush wife is 10 years more than Ayush present age. The family consists of four people and the average of their present ages is 30.25 years. All ages are in years. Concept / Approach: We proceed by expressing each family member age in terms of Ayush age A. First, we convert the percentage relation into an algebraic expression for the son age. Next, we use the information from four years ago to express the daughter age in terms of the son age. Then we express the wife age from the given sum with the daughter. Finally, we use the average to get the total sum of all ages and form an equation in A. Solving this equation gives Ayush present age, which we can then verify against all conditions. Step-by-Step Solution: Step 1: Let Ayush present age be A years. Step 2: After subtracting 6 years from A, we get A - 6. The present age of the son is 25 percent of this, so son age S = 25 percent of (A - 6) = (A - 6) / 4. Step 3: Four years ago, the son age was S - 4 and the daughter age was D - 4, where D is the daughter present age. Step 4: At that time, the daughter age was 7 years more than the son age, so D - 4 = (S - 4) + 7, which simplifies to D = S + 7. Step 5: The sum of the present ages of the daughter and the wife is 10 years more than Ayush present age, so D + W = A + 10, where W is the wife present age. Step 6: Substitute D = S + 7 into this to get S + 7 + W = A + 10, which gives W = A + 3 - S. Step 7: The average age of the four family members is 30.25 years, so the total of their present ages is 4 * 30.25 = 121 years. Step 8: The total sum is A (Ayush) + W (wife) + S (son) + D (daughter) = 121. Step 9: Substitute W = A + 3 - S and D = S + 7 into this total: A + (A + 3 - S) + S + (S + 7) = 121. Step 10: Simplify: A + A + 3 - S + S + S + 7 = 2A + S + 10 = 121. Step 11: So 2A + S = 111. Step 12: But S = (A - 6) / 4, so substitute to get 2A + (A - 6) / 4 = 111. Step 13: Multiply through by 4 to clear the denominator: 8A + (A - 6) = 444. Step 14: Combine like terms: 9A - 6 = 444, giving 9A = 450. Step 15: Divide both sides by 9 to obtain A = 50. Step 16: Therefore Ayush present age is 50 years. Verification / Alternative check: Let us verify all relations. If A = 50, then S = (50 - 6) / 4 = 44 / 4 = 11 years. The daughter age is D = S + 7 = 11 + 7 = 18 years. The wife age is W = A + 3 - S = 50 + 3 - 11 = 42 years. Total present ages are 50 + 42 + 11 + 18 = 121 years, and the average is 121 / 4 = 30.25 years, as specified. Four years ago, the son was 7 years old and the daughter was 14 years old, so the daughter was indeed 7 years older than the son. All conditions are satisfied, confirming the correctness of the solution. Why Other Options Are Wrong: Option A (45 years) fails to produce an average of 30.25 years when the corresponding family ages are calculated from the given relations. Option C (60 years) leads to inconsistent values for the son or daughter ages or breaks the condition about the daughter and wife sum. Option D (40 years) similarly does not satisfy all the given relations and the average simultaneously. Common Pitfalls: This question contains many statements, so it is easy to lose track of the relationships or to misinterpret the percentage condition. Some students also incorrectly apply the average formula, forgetting that it is the total divided by the number of people. To avoid these pitfalls, write each relation algebraically step by step, keep all expressions in terms of a single variable and only then solve the final equation. Checking all conditions at the end is essential to ensure there are no hidden mistakes. Final Answer: The present age of Ayush is 50 years.

Question 15

Three years from now, the age of Dharitri will be eight years less than twice the age of Eunice at that time. The sum of their present ages is 61 years. What is the present age, in years, of Dharitri?

Accepted Answer

Introduction / Context: This age problem uses a relationship between future ages and the current sum of ages. It illustrates how to interpret statements like “eight years less than twice the age” and translate them into algebraic equations. Such problems often appear in reasoning sections to evaluate your skill in forming and solving simultaneous linear equations. Given Data / Assumptions: Three years from now, Dharitri age will be eight years less than twice Eunice age at that time. The sum of their present ages is 61 years. We need to find the present age of Dharitri. Ages are in years and are positive. Concept / Approach: We start by assigning variables to the present ages of Dharitri and Eunice. Then we write expressions for their ages three years in the future. The phrase “eight years less than twice” is carefully translated into an equation involving these future ages. Combined with the equation for the present sum of ages, this gives a system of two equations in two unknowns. Solving this system yields the present ages, from which we extract the required value. Step-by-Step Solution: Step 1: Let the present age of Dharitri be D years and the present age of Eunice be E years. Step 2: Three years from now, Dharitri age will be D + 3 years. Step 3: Three years from now, Eunice age will be E + 3 years. Step 4: The statement says that in three years, Dharitri age will be eight years less than twice Eunice age at that time. This gives the equation D + 3 = 2 * (E + 3) - 8. Step 5: Expand the right side: D + 3 = 2E + 6 - 8 = 2E - 2. Step 6: So we have the first equation: D + 3 = 2E - 2. Step 7: We also know that the sum of their present ages is 61 years, so D + E = 61. This is the second equation. Step 8: From D + 3 = 2E - 2, rearrange to get D = 2E - 5. Step 9: Substitute D = 2E - 5 into D + E = 61 to get (2E - 5) + E = 61. Step 10: Simplify: 3E - 5 = 61, so 3E = 66 and E = 22. Step 11: Substitute E = 22 into D = 2E - 5 to get D = 2 * 22 - 5 = 44 - 5 = 39. Step 12: Therefore, Dharitri present age is 39 years. Verification / Alternative check: Check the conditions with D = 39 and E = 22. The sum of present ages is 39 + 22 = 61 years, which matches the given sum. Three years from now, Dharitri will be 42 years old and Eunice will be 25 years old. Twice Eunice age at that time is 2 * 25 = 50, and eight years less than this is 50 - 8 = 42, which equals Dharitri age after three years. Both statements are satisfied, confirming that the solution is correct. Why Other Options Are Wrong: Option A (41 years) leads to an incorrect sum or fails the future age relation when Eunice corresponding age is calculated. Option C (36 years) does not produce 61 as the total present age when combined with a consistent age of Eunice that satisfies the future condition. Option D (43 years) similarly fails either the future relationship or the present age sum requirement. Common Pitfalls: A common error is misinterpreting the phrase “eight years less than twice Eunice age” and writing D + 3 = 2E + 3 - 8 instead of correctly considering both future ages. Another mistake is to forget to increment both ages by 3 when moving to the future time. Writing each step clearly and using separate symbols for present and future ages helps avoid confusion. Final Answer: The present age of Dharitri is 39 years.

Question 16

The present ages of a father and his son are 48 years and 28.8 years respectively. The father says to his son, “I was a certain fraction of your present age when you were born.” What fraction of the son present age was the father age when the son wa…

Accepted Answer

Introduction / Context: This problem is about relating present ages to ages at the time of birth using fractions. The father compares his age at the time his son was born to the son present age. Such questions reinforce understanding of how age differences remain constant over time and how to express one quantity as a fraction of another. Given Data / Assumptions: The present age of the father is 48 years. The present age of the son is 28.8 years. We need to find what fraction of the son present age the father age was at the time of the son birth. Ages are in years, and fractional ages are allowed. Concept / Approach: The key concept is that the difference between the father age and the son age remains constant throughout their lives. To find the father age when the son was born, we subtract the son present age from the father present age. After that, we compare this age to the son present age by forming a fraction. Simplifying the fraction using basic arithmetic then lets us match it to the given options like half, two third and so on. Step-by-Step Solution: Step 1: The present age of the father is 48 years and the present age of the son is 28.8 years. Step 2: At the time the son was born, his age was 0, so the number of years that have passed since then is equal to the son present age, 28.8 years. Step 3: Therefore, at the time of the son birth, the father age was 48 - 28.8 years. Step 4: Compute this difference: 48 - 28.8 = 19.2 years. Step 5: We must express 19.2 as a fraction of the son present age 28.8. Step 6: Form the fraction 19.2 / 28.8. Step 7: Simplify this fraction. Divide numerator and denominator by 9.6 to get (19.2 / 9.6) / (28.8 / 9.6) = 2 / 3. Step 8: So the father age at the son birth was two third of the son present age. Verification / Alternative check: Consider that two third of the son present age 28.8 is (2 / 3) * 28.8 = 19.2 years. Adding the time since the son birth, which is 28.8 years, to this 19.2 gives 19.2 + 28.8 = 48 years, which is exactly the father present age. This confirms that our fraction is correct and consistent with the ages given in the question. Why Other Options Are Wrong: Option A (half) would mean the father was 14.4 years old at the son birth, which is not consistent with the actual difference between the present ages. Option C (one-fifth) would give a father age of 5.76 years at the birth, which is impossible and clearly inconsistent. Option D (one-third) would make the father 9.6 years old at the birth, which again does not match the given values or realistic age differences. Common Pitfalls: Some students mistakenly divide the present age difference by the father age instead of the son present age, or they may attempt to use the wrong base for the fraction. Another common mistake is to misinterpret the phrase “when you were born” and incorrectly use the son present age instead of the father age at that time. Carefully following the timeline and using the age difference concept helps avoid these errors. Final Answer: The father age at the time of the son birth was two-third of the son present age.

Question 17

There were 24 students in a class. One student who was 18 years old left the class and was replaced by a new student. As a result, the average age of the class was lowered by 1 month. What is the age, in years, of the new student?

Accepted Answer

Introduction / Context: This question deals with averages and how they change when one data point is replaced by another. It is a standard example from the topic of average age and is often seen in quantitative aptitude exams. The key idea is to understand how total age is affected by the exit of one student and the entry of a new one, and how this translates into a change in the average. Given Data / Assumptions: Initially, there are 24 students in the class. One student aged 18 years leaves the class. A new student joins the class in place of the student who left. The average age of the class decreases by 1 month, which is 1 / 12 of a year. We must find the age of the new student in years. Concept / Approach: The average age is the total age divided by the number of students. Since the number of students remains 24, the change in the average gives us direct information about the change in total age. A decrease of 1 month in average age means a decrease of 1 month multiplied by 24 in the total age. This decrease is caused by replacing the 18 year old student with the new student. We equate the change in total age to the difference in ages of the leaving and entering students to solve for the unknown age. Step-by-Step Solution: Step 1: Let the original average age of the 24 students be A years. Step 2: Then the original total age of the class is 24A years. Step 3: When the 18 year old student leaves and the new student of age x years joins, the number of students remains 24. Step 4: The new average age becomes A minus 1 month, that is A - 1 / 12 years. Step 5: The new total age of the class is 24 * (A - 1 / 12) = 24A - 2 years, because 24 * (1 / 12) = 2. Step 6: The new total age is also equal to the old total age minus 18 plus x, that is 24A - 18 + x. Step 7: Equate these two expressions: 24A - 18 + x = 24A - 2. Step 8: Cancel 24A from both sides to obtain -18 + x = -2. Step 9: Add 18 to both sides to get x = -2 + 18 = 16. Step 10: Therefore, the age of the new student is 16 years. Verification / Alternative check: We can interpret the result directly. Since the average decreased by 1 month for 24 students, the total age decreased by 2 years. This decrease must come from replacing the 18 year old student with the new student, so the new student must be 2 years younger than the old one. Thus the new student age is 18 - 2 = 16 years, which matches our algebraic solution. This verifies that the answer is consistent. Why Other Options Are Wrong: Option A (14 years) would represent a decrease of 4 years for the one student change, leading to a drop in average of 4 / 24 years, which is greater than 1 month. Option B (15 years) would give a 3 year difference and thus a larger decrease in the average than the stated 1 month. Option D (17 years) would produce only a 1 year change, causing a smaller drop in average than required, so it is also incorrect. Common Pitfalls: Students often forget to convert months into years, or they mistakenly multiply by the wrong number of students when computing the change in total age. Another frequent error is to treat the new average as A + 1 / 12 instead of A - 1 / 12. Carefully converting all units to years and writing out the total age equations step by step helps avoid these issues. Final Answer: The age of the new student is 16 years.

Question 18

The present age of Rakhi is twelve times the present age of her daughter Anubha. If Anubha is 3 years old now, what was the age of Rakhi, in years, two years ago?

Accepted Answer

Introduction / Context: This is a straightforward ages question that relates the present age of a mother to the present age of her daughter by a simple multiple. It then asks for the mother age two years in the past. Problems like this are commonly used to introduce learners to the idea of proportional relationships in age based questions. Given Data / Assumptions: Rakhi present age is twelve times the present age of her daughter Anubha. Anubha present age is 3 years. We need to find Rakhi age two years ago. Ages are in years and non negative. Concept / Approach: We first calculate Rakhi present age by multiplying Anubha age by the given factor of twelve. Then, since two years ago is in the past, we subtract two years from Rakhi present age to find the required value. This is a direct application of the idea that present ages are related by a constant multiple, and time shifts apply equally to both people, although the question here only asks for Rakhi past age. Step-by-Step Solution: Step 1: Anubha present age is 3 years. Step 2: Rakhi present age is given as twelve times the age of Anubha. Step 3: So Rakhi present age is 12 * 3 = 36 years. Step 4: We are asked for Rakhi age two years ago. Step 5: Two years ago, her age would have been 36 - 2 = 34 years. Step 6: Therefore, Rakhi age two years earlier was 34 years. Verification / Alternative check: We can check quickly by thinking forwards. If Rakhi was 34 years old two years ago, then adding two years gives 36 years as her present age. Anubha is 3 years old now, and 12 times 3 is indeed 36, matching the description that Rakhi present age is twelve times Anubha present age. This confirms the correctness of the answer. Why Other Options Are Wrong: Option A (20 years) is far too small; adding two years gives a present age of 22 which is not twelve times 3. Option C (30 years) would make Rakhi 32 years old now, which is not equal to 36 years, so the relation fails. Option D (36 years) represents Rakhi present age, not her age two years ago, so it does not answer the question asked. Common Pitfalls: Some learners misread the question and report the present age instead of the age two years ago. Others may confuse which age needs to be multiplied or forget to subtract the two years. Always pay attention to whether the question is about present, past or future age, and double check that you have applied the time shift in the correct direction. Final Answer: Rakhi age two years earlier was 34 years.

Question 19

Five years ago, the average age of a family consisting of a father, a mother and a son was 35 years. Three years ago, the average age of the father and the mother was 46 years. What is the present age, in years, of the son?

Accepted Answer

Introduction / Context: This question combines average age information at two different times for a small family. It is a standard type of problem where the average of all three members is given for one time in the past, and the average of only the parents is given for another time. From this information, we have to deduce the current age of the son. It requires careful use of the average formula and the understanding that all members age equally over time. Given Data / Assumptions: Five years ago, the family consisted of father, mother and son and their average age was 35 years. Three years ago, the average age of the father and the mother alone was 46 years. We need the present age of the son. Ages are measured in years and are positive. Concept / Approach: We use the average at each time to calculate the total ages of the corresponding group. At five years ago, we get the combined total of all three. At three years ago, we get the combined total of the parents only. By moving these totals forward to the present time by adding the appropriate number of years for each person, we can find the present total of all three and the present total of the parents. The difference between these totals gives the present age of the son. Step-by-Step Solution: Step 1: Five years ago, the average age of the father, mother and son was 35 years for 3 people. Step 2: The total age of the three family members five years ago was 35 * 3 = 105 years. Step 3: From five years ago to the present, each of the three persons has aged 5 years, increasing the total age by 3 * 5 = 15 years. Step 4: Therefore, the total present age of the three family members is 105 + 15 = 120 years. Step 5: Three years ago, the average age of the father and the mother was 46 years for 2 people. Step 6: The combined age of the parents three years ago was 46 * 2 = 92 years. Step 7: From three years ago to now, both parents have aged 3 years each, so the total age of the parents has increased by 2 * 3 = 6 years. Step 8: Hence the present combined age of the father and the mother is 92 + 6 = 98 years. Step 9: The present age of the son is obtained by subtracting the parents present total from the family present total: 120 - 98 = 22 years. Step 10: Therefore, the son present age is 22 years. Verification / Alternative check: We can check by reconstructing the ages backwards. If the son present age is 22 years, then five years ago he was 17 years old. Suppose the present total of the parents is 98 years, so five years ago their combined age was 98 - 10 = 88 years. At that time, the total age of the family was 88 + 17 = 105 years, matching the earlier calculation of 105. Three years ago, the parents combined age would have been 98 - 6 = 92 years, giving an average of 92 / 2 = 46 years, which agrees with the given data. This confirms the solution. Why Other Options Are Wrong: Option A (20 years) does not produce consistent totals when checked against both average conditions. Option B (24 years) gives a different present total, and when taken back five and three years, breaks at least one of the average relationships. Option C (26 years) also fails to satisfy both the five year and three year average constraints simultaneously. Common Pitfalls: Students may incorrectly apply the average formula or forget to add the correct number of years to move from a past time to the present. Another common mistake is to assume that the average remains constant over time, which is not the case here. Always compute total ages first from averages, then adjust those totals by adding or subtracting the appropriate time for each person before making comparisons. Final Answer: The present age of the son is 22 years.

Question 20

The present age of A is twice the present age of B. After 8 years, the age of B will be four times the present age of C. If C celebrated his fifth birthday 9 years ago, what is the present age, in years, of A?

Accepted Answer

Introduction / Context: This age problem connects three people, A, B and C, through simple relationships involving multiples and a time shift. The age of C is given indirectly through a birthday reference in the past. Such questions are common in aptitude tests to assess whether you can decode age information spread across different time points and assemble it into a coherent set of equations. Given Data / Assumptions: The present age of A is twice the present age of B. After 8 years, the age of B will be four times the present age of C. C celebrated a fifth birthday 9 years ago. We must find the present age of A. Ages are given in years and are positive. Concept / Approach: We start by determining the present age of C from the statement about the fifth birthday. Then we use the future relation of B age after 8 years in terms of C present age to find B present age. Finally, we use the relation that A is twice B to find A present age. This approach shows how to step through a chain of age relationships in a logical order. Step-by-Step Solution: Step 1: C celebrated a fifth birthday 9 years ago. Step 2: That means 9 years ago C age was 5 years. Step 3: Therefore, C present age is 5 + 9 = 14 years. Step 4: After 8 years, B age will be four times C present age. Step 5: C present age is 14 years, so after 8 years B age will be 4 * 14 = 56 years. Step 6: If B age after 8 years is 56 years, then B present age is 56 - 8 = 48 years. Step 7: A present age is twice the present age of B. Step 8: Therefore A present age is 2 * 48 = 96 years. Step 9: Hence, A is 96 years old now. Verification / Alternative check: Verify each relation with the obtained ages. C is 14 years old now, so 9 years ago C was 14 - 9 = 5 years old, matching the birthday information. B is 48 years old now, so after 8 years B will be 48 + 8 = 56 years old. Four times C present age is 4 * 14 = 56 years, which matches B future age. A present age is 96 years, which is exactly twice 48, confirming the relation between A and B. All conditions in the problem are satisfied. Why Other Options Are Wrong: Option A (88 years) would mean B present age is 44, and then B age after 8 years would not equal four times C age, so the condition fails. Option C (92 years) similarly gives inconsistent values for B and C when checked against the given relationships. Option D (84 years) fails to make A exactly twice the correct B age that fits the relation with C. Common Pitfalls: Learners sometimes misread the statement about the fifth birthday and treat 5 years as the current age rather than the age 9 years ago. Another error is to apply the multiple 4 to B present age instead of B future age as specified. Carefully reading each time reference and applying the correct order of operations is crucial for solving such age chain problems accurately. Final Answer: The present age of A is 96 years.

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