Question 1

The ratio of the present ages of K and M is 4:5. The difference between M's present age and K's age 5 years from now is 3 years. Find (1) the difference between their present ages and (2) the total of their present ages.

Accepted Answer

Introduction:This question tests using a present-age ratio along with a future-based difference statement. The ratio 4:5 suggests expressing ages as 4x and 5x. The second condition gives an exact numeric difference involving a time shift (K after 5 years). Once x is found, both the present difference and present sum can be computed directly. Given Data / Assumptions: Present ratio K : M = 4 : 5 Let K = 4x and M = 5x Condition: M (present) - (K after 5 years) = 3 We need present difference (M - K) and present sum (M + K) Concept / Approach:Use ratio representation. Convert the future difference statement into an equation: 5x - (4x + 5) = 3. Solve for x, then compute difference and sum. Step-by-Step Solution:Let K = 4x and M = 5xK after 5 years = 4x + 5Given: 5x - (4x + 5) = 35x - 4x - 5 = 3x - 5 = 3 => x = 8K = 4x = 32, M = 5x = 40Present difference = 40 - 32 = 8Present sum = 40 + 32 = 72 Verification / Alternative check:K after 5 years is 37. M present is 40. Difference 40 - 37 = 3 matches the given statement. So both ages are correct, hence difference and sum are correct. Why Other Options Are Wrong:10 and 60: implies ages 25 and 35, but 35 - (25+5) = 5, not 3.12 and 84: implies larger x which breaks the 3-year condition.16 and 65: inconsistent because with ratio 4:5, sum must be 9x (a multiple of 9).6 and 54: gives x=6, then 5x - (4x+5) = 6 - 5 = 1, not 3. Common Pitfalls:Using present difference instead of the future-shifted difference in the equation.Adding 5 years to M instead of only to K.Forgetting the question asks for both difference and total. Final Answer:8 years and 72 years

Question 2

Sunitha and Pranitha are 40 years and 60 years old respectively at present. How many years ago was the ratio of their ages exactly 3:5?

Accepted Answer

Introduction:This question checks how to handle age ratios in the past. When we go back by t years, both people's ages reduce by the same t. So if Sunitha is 40 and Pranitha is 60 now, then t years ago they were (40 - t) and (60 - t). The ratio condition (40 - t)/(60 - t) = 3/5 gives a single equation in t, which can be solved using cross-multiplication. Given Data / Assumptions: Sunitha's present age = 40 years Pranitha's present age = 60 years t years ago, ratio was 3 : 5 So (40 - t)/(60 - t) = 3/5 Concept / Approach:Use past ages with variable t and solve the ratio equation by cross-multiplying. Step-by-Step Solution:t years ago, ages were: 40 - t and 60 - tGiven ratio: (40 - t)/(60 - t) = 3/5Cross-multiply: 5(40 - t) = 3(60 - t)200 - 5t = 180 - 3t200 - 180 = 5t - 3t20 = 2t => t = 10 Verification / Alternative check:10 years ago: Sunitha was 30 and Pranitha was 50. Ratio 30:50 simplifies to 3:5, which matches the condition exactly. Why Other Options Are Wrong:15 years: would give ages 25 and 45, ratio 25:45 = 5:9, not 3:5.18 years: gives 22 and 42, ratio 11:21, not 3:5.24 years: gives 16 and 36, ratio 4:9, not 3:5.12 years: gives 28 and 48, ratio 7:12, not 3:5. Common Pitfalls:Subtracting different values from each age instead of the same t.Using 40/60 = 2/3 and confusing it with the required 3/5 ratio.Not simplifying the ratio after computing past ages. Final Answer:10 years

Question 3

Karthik is currently 32 years old and his son is 7 years old. After how many years from now will Karthik be exactly twice as old as his son?

Accepted Answer

Introduction / Context: This is a classic problems on ages question from quantitative aptitude. It checks whether you can translate a simple English statement about present and future ages into an equation in one variable and then find the time after which one person becomes a multiple of another person age. Such questions are very common in bank exams, campus placements, and other competitive tests. Given Data / Assumptions: Karthik present age is 32 years. His son present age is 7 years. We need the number of years from now after which Karthik age will be exactly twice the age of his son. Both ages increase at the same rate, that is by the same number of years as time passes. Concept / Approach: The key idea in problems on ages is to define a variable for the unknown quantity, usually the present age or the required time. Then we express future or past ages in terms of this variable and form an equation from the given condition. Here the condition is that after some years, the father age becomes twice the son age. That single relationship leads to one linear equation in one variable, which is easy to solve using basic algebra. Finally, we verify by substituting the result back into the condition. Step-by-Step Solution: Step 1: Let the required number of years from now be t. Step 2: After t years, Karthik age will be 32 + t. Step 3: After the same t years, the son age will be 7 + t. Step 4: The condition says that at that time, father age is twice the son age, so set up the equation 32 + t = 2 × (7 + t). Step 5: Solve this linear equation to get the value of t, which comes out to 18. Step 6: Therefore, after 18 years, Karthik age will be twice his son age. Verification / Alternative check: After 18 years, Karthik age will be 32 + 18 = 50 years. His son age will be 7 + 18 = 25 years. Now check the relationship: 50 is exactly 2 times 25, so the condition is perfectly satisfied. This confirms that the equation was set correctly and that no logical mistake was made in interpreting the wording of the question. Why Other Options Are Wrong: Option 25: After 25 years, ages would be 57 and 32, and 57 is not twice 32, so this is incorrect. Option 7: After 7 years, ages would be 39 and 14, and 39 is not twice 14, so this is incorrect. Option 15: After 15 years, ages would be 47 and 22, and 47 is not twice 22, so this is also incorrect. Option 20: After 20 years, ages would be 52 and 27, and 52 is not twice 27, so this fails the condition as well. Common Pitfalls: A common mistake is to try to make the present age of Karthik twice the present age of his son, which is not what the question says. Another frequent error is to write the wrong equation, for example 32 + t = 2 × 7 + t, which misses the fact that the son age also increases by t. Always ensure that all people ages move forward or backward by the same number of years when you deal with future or past situations. Final Answer: The required number of years after which Karthik will be twice as old as his son is 18 years.

Question 4

The difference between the present ages of Avanthi and Kapil is 9 years. After 7 years, Kapil age will be twice the age of Avanthi. What will be Kapil age after 4 years from now?

Accepted Answer

Introduction / Context: This problem on ages involves two people and a mix of present and future ages. Such questions test your ability to convert verbal statements into simultaneous equations and then to extract the exact value requested, which here is Kapil age after a certain number of years. The question also trains you to handle the phrase twice the age carefully, which indicates a multiplication relationship rather than a simple difference. Given Data / Assumptions: The difference between the present ages of Avanthi and Kapil is 9 years. After 7 years, Kapil age will be twice the age of Avanthi at that time. We need to find Kapil age after 4 years from now. Ages are measured in whole years and both people age normally over time. Concept / Approach: Whenever you see words like twice, three times, or difference of ages, it suggests setting up algebraic equations. Let the present ages be variables, use the difference condition to form one equation, and use the future double age condition to form another equation. Solving these two linear equations in two variables gives the present ages. Then it is easy to move forward in time to find Kapil age after 4 years. The main skill is careful translation of the words into correct algebraic expressions. Step-by-Step Solution: Step 1: Let the present age of Avanthi be A years and the present age of Kapil be K years. Step 2: Use the difference condition to write K − A = 9, assuming Kapil is older. Step 3: After 7 years, Avanthi age becomes A + 7 and Kapil age becomes K + 7. Step 4: The statement that after 7 years Kapil age is twice Avanthi age becomes K + 7 = 2 × (A + 7). Step 5: Solve the pair of equations K − A = 9 and K + 7 = 2 × (A + 7). You will obtain A = 2 and K = 11. Step 6: Kapil age after 4 years will be K + 4 = 11 + 4 = 15 years. Verification / Alternative check: Check with the found ages. At present Kapil is 11 and Avanthi is 2, so the difference is 9 years as given. After 7 years, Kapil will be 18 and Avanthi will be 9, and 18 is exactly twice 9. After 4 years, Kapil will indeed be 15 years old. All conditions match the problem statement, so the solution is consistent. Why Other Options Are Wrong: Option 16: This would imply Kapil present age is 12, which breaks the given relationships. The future double condition would not hold. Option 18: If Kapil age after 4 years were 18, his present age would be 14, again failing the given conditions when checked. Option 20: This would mean Kapil is 16 now; substituting into the equations does not satisfy the difference and double constraints. Option 22: This would make Kapil even older, and checking with the algebra shows the data cannot all be satisfied at once. Common Pitfalls: Learners often confuse who is older and write A − K = 9 instead of K − A = 9. Another mistake is to forget that both ages increase by the same amount when you move several years into the future, so some people write incorrect expressions such as K + 7 = 2A. Always express the age at a future time as present age plus the number of years, and only then apply the multiple relationship. Final Answer: Kapil age after 4 years will be 15 years.

Question 5

Manogna father was 38 years old when she was born, while her mother was 36 years old when her brother, who is 4 years younger than Manogna, was born. What is the difference between the ages of her parents in years?

Accepted Answer

Introduction / Context: This problems on ages question focuses on relative ages within a family. Instead of asking for an absolute age, it asks for the difference between the ages of the parents, using information from the times when their children were born. Such questions test your understanding of how age differences remain constant over time and how to interpret statements about being younger or older by a certain number of years. Given Data / Assumptions: When Manogna was born, her father was 38 years old. Her brother is 4 years younger than Manogna. When the brother was born, the mother was 36 years old. We need the difference between the ages of the father and the mother. Age differences between adults remain constant over time. Concept / Approach: Key points in this type of problem are that age differences between the same two people do not change as years pass, and that birth events fix specific moments in time with known ages. We can express parent ages in terms of the current age of Manogna and then subtract to find the constant difference between the father and the mother. An algebraic approach is convenient but a timeline or reasoning with differences also works very well for such family based age puzzles. Step-by-Step Solution: Step 1: Let the present age of Manogna be M years. Step 2: At the time of her birth, the father was 38 years older than the newborn, so the present age of the father is M + 38. Step 3: The brother is 4 years younger than Manogna, so his present age is M − 4 years. Step 4: At the time of the brother birth, the mother was 36 years older than the newborn, so the present age of the mother is (M − 4) + 36 = M + 32 years. Step 5: The age difference between the parents is therefore (M + 38) − (M + 32) = 6 years. Verification / Alternative check: Notice that we did not actually need the exact present age of either parent or of the children. Since both ages were written in terms of M, that variable cancels out in the subtraction, leaving a constant difference of 6 years. This is consistent at all times in the past, present, and future, and it shows that the father is always 6 years older than the mother. You can choose any sample value for M to test and you will always get the same difference. Why Other Options Are Wrong: Option 2 years: This would mean the father is only slightly older than the mother, which does not agree with the calculations derived from the birth information. Option 4 years: This difference also does not match the derived expressions for the parent ages when carefully written. Option 8 years and Option 10 years: These values are larger than the true difference. Substituting them back into hypothetical ages for the parents does not match the conditions given at the two birth times. Common Pitfalls: Many learners try to track exact present ages and get lost in the details, or they incorrectly think that the stated numbers change over time. The most robust method is to express all relevant ages in terms of a simple variable, like the present age of one child, and remember that the age gap between the parents is fixed. Also, be careful with younger than and older than wording, which can be reversed by mistake if read too fast. Final Answer: The difference between the ages of Manogna parents is 6 years.

Question 6

The ratio of the present ages of L and N is 7 : 5. If the age of N after seven years will be 32 years, then what is the present age in years of L?

Accepted Answer

Introduction / Context: This is a straightforward ratio based problem on ages. It combines a given ratio of present ages with one absolute value for a future age, and from this you have to find one person present age. Such questions check your ability to use a ratio variable, link it with an actual numeric future age, and then scale the ratio correctly. They are very common in aptitude tests because they check conceptual understanding more than heavy calculations. Given Data / Assumptions: The ratio of the present ages of L and N is 7 : 5. After 7 years, the age of N will be 32 years. We are asked to find the present age of L in years. Both people ages increase in a normal way, with the same number of years added over time. Concept / Approach: When ages are in a ratio like 7 : 5, we represent the actual ages as multiples of a common variable. Using that representation and any extra condition, such as a known future or past age, we can find the value of the common multiplier. Once that multiplier is known, the present ages follow directly. In this question, we only need one equation because the future age of N is given exactly, and that is enough to compute the variable and then L age. Step-by-Step Solution: Step 1: Let the present ages of L and N be 7k and 5k respectively, where k is a positive number. Step 2: After 7 years, N age will be 5k + 7. Step 3: We are told that 5k + 7 equals 32 years. Step 4: Solve 5k + 7 = 32 to obtain 5k = 25 and hence k = 5. Step 5: Substitute k into L age, so L present age is 7k = 7 × 5 = 35 years. Verification / Alternative check: Check the ratio using the found ages. If L is 35 and N is 25 at present, the ratio 35 : 25 simplifies to 7 : 5, which matches the given ratio. After 7 years, N age becomes 25 + 7 = 32 years, which is also exactly the future age stated in the question. Therefore the value 35 years for L is fully consistent with all conditions, and the solution is correct. Why Other Options Are Wrong: Option 49: If L were 49 years old, N would be 35 years old to keep the 7 : 5 ratio. Then after 7 years, N would be 42, not 32, so this is incorrect. Option 28: With L as 28, N would be 20. After 7 years, N would be 27, which again does not match 32 years. Option 42: In this case N would be 30 initially and 37 after 7 years, still not 32. Option 30: This does not even preserve the ratio of 7 : 5 when paired with any simple value for N, so it fails the first condition itself. Common Pitfalls: Students sometimes wrongly add years only to one person or forget to add the same number of years to both when dealing with future ages. Another frequent mistake is to directly treat 7 and 5 as ages instead of as ratio parts. Always express the actual ages as 7k and 5k, then use the extra information to find k. Checking the ratio at the end is a good habit to avoid careless slips. Final Answer: The present age of L is 35 years.

Question 7

The ratio of the present ages of Rasika and Shami is 7 : 5. After 17 years the ratio of their ages will be 12 : 11. What is Rasika present age in years?

Accepted Answer

Introduction / Context: This question is a classic two time ratio problem on ages. It gives the ratio of present ages and the ratio of ages after a certain number of years. From these two ratios you must determine the actual present age of one person. Such questions help test algebraic skills, especially forming equations from ratios and understanding how adding a constant number of years affects both numerator and denominator in an age ratio. Given Data / Assumptions: The present age ratio of Rasika to Shami is 7 : 5. After 17 years, the ratio of their ages will be 12 : 11. We are asked to find the present age of Rasika. Both Rasika and Shami age in a normal way, each gaining 17 years over the given period. Concept / Approach: When a problem gives the ratio of present ages and another ratio many years later, the standard method is to represent the present ages using a common variable, and then write an equation for the future ratio. The future ratio expression will involve the same variable plus the added years. Solving this equation yields the value of the variable and thus the actual ages. This approach works because age is linear with time and both ages increase by the same constant amount over the same period. Step-by-Step Solution: Step 1: Let the present ages of Rasika and Shami be 7k and 5k respectively. Step 2: After 17 years, Rasika age becomes 7k + 17 and Shami age becomes 5k + 17. Step 3: According to the question, the ratio (7k + 17) : (5k + 17) is equal to 12 : 11. Step 4: Form the equation (7k + 17) / (5k + 17) = 12 / 11 and solve this linear equation for k. Step 5: Solving gives k = 1, so Rasika present age is 7k = 7 years. Verification / Alternative check: If Rasika is 7 years old at present, then Shami current age is 5 years. After 17 years, Rasika age will be 7 + 17 = 24 years and Shami age will be 5 + 17 = 22 years. The ratio 24 : 22 simplifies to 12 : 11, which exactly matches the future ratio given in the question. Therefore, the derived value of 7 years is fully consistent with the data, even though it may look small for a typical person name, the mathematics is correct for the puzzle. Why Other Options Are Wrong: Option 5: If Rasika were 5 years old, Shami would be about 3.57 years old from the ratio, which does not yield a neat future ratio of 12 : 11 when 17 years are added. Option 80: This would make Shami age large as well, and the resulting future ratio would not be 12 : 11. Option 16: If Rasika age were 16, Shami age would be 16 × 5 ÷ 7 which is not an integer, and the future ratio would not match. Option 28: Similar tests show that this does not preserve the stated ratios either. Common Pitfalls: Learners sometimes mix up which person corresponds to which part of the ratio or forget that 17 years must be added to both ages in the future scenario. Another common mistake is to treat 7 and 5 as actual ages instead of 7k and 5k, which prevents you from satisfying both present and future ratios simultaneously. Always set up a clean fraction equation and cross multiply carefully to avoid algebraic slips. Final Answer: Rasika present age is 7 years.

Question 8

If twice Reena present age is subtracted from four times her age three years from now, the result is equal to three times her age three years ago. What will be Reena age after one year from now?

Accepted Answer

Introduction / Context: This is a classic algebraic age puzzle that involves present, past, and future ages in one statement. The sentence looks complicated, but it is simply describing a relationship between linear expressions of the same unknown age at different times. Questions like this are meant to test whether you can carefully decode the language into an equation and then solve for the present age before answering what the age will be after a given number of years. Given Data / Assumptions: Reena has some unknown present age. Four times her age three years from now is considered. Twice her present age is subtracted from that quantity. The result equals three times her age three years ago. We have to find Reena age one year from now. Concept / Approach: To solve such a question, define a variable for Reena present age. Then write expressions using this variable for her age three years from now and three years ago. Apply the multipliers indicated by four times, twice, and three times, and then convert the verbal condition into a clear algebraic equation. Once that linear equation is solved, you obtain Reena present age. From there, calculating her age after one year is straightforward. The main challenge is reading the sentence slowly and placing the operations in the correct order. Step-by-Step Solution: Step 1: Let Reena present age be x years. Step 2: Her age three years from now will be x + 3 years. Step 3: Four times her age three years from now is 4 × (x + 3). Step 4: Twice her present age is 2x, and this is subtracted from 4 × (x + 3). Step 5: Her age three years ago is x − 3, and three times that is 3 × (x − 3). The condition states 4 × (x + 3) − 2x = 3 × (x − 3). Step 6: Solve this equation to get x = 21 years, so Reena present age is 21 years, and her age after one year will be 22 years. Verification / Alternative check: Take Reena present age as 21 years. Three years from now she will be 24; four times that is 96. Twice her present age is 42, and 96 − 42 = 54. Three years ago she was 18 and three times that is also 54. Since both sides match, the equation is satisfied and the present age 21 years is correct. Therefore, one year from now she will be 22 years old, which answers the question correctly. Why Other Options Are Wrong: Option 21 yrs: This is her current age, not her age after one year, so it does not answer the final question. Option 20 yrs: If we assume 20, the equation does not balance, because the computed values on each side differ. Option 24 yrs: This would correspond to an incorrect present age and fails the relationship when tested. Option 18 yrs: This is too low; substituting 18 years into the equation does not satisfy the condition. Common Pitfalls: Many students misread the order of operations and accidentally treat four times three years from now as adding 12 years instead of multiplying the future age by 4. Another common error is to subtract three years instead of adding or vice versa when dealing with phrases like three years from hence and three years before. To avoid these mistakes, sketch a simple timeline, label the present, past, and future ages, and then attach the multipliers only after you have written those expressions correctly. Final Answer: Reena age after one year will be 22 years (that is, option 22 yrs).

Question 9

Person A is two years older than person B, and B is twice as old as person C. If the total of the present ages of A, B and C is 27 years, then how old is B now?

Accepted Answer

Introduction / Context: This age puzzle involves three related people, where the ages are connected by simple linear relationships. One person is older than another by a fixed number of years, and one is a multiple of someone else age. The sum of all three present ages is given. Questions like this are very common in aptitude exams and practice tests because they combine logical reasoning with elementary algebra and test whether you can set up and solve equations with several variables. Given Data / Assumptions: Person A is two years older than person B. Person B is twice as old as person C. The total of the present ages of A, B and C is 27 years. We have to determine the present age of person B. All ages are present ages, and we do not deal with past or future times. Concept / Approach: The best way to handle this question is to introduce a variable for the simplest age, which is usually the youngest person. Here the age of C is the natural choice. Then we express B as twice that variable and A as B plus two years. This gives three expressions for each person age in terms of the same variable. Summing them and equating to the total age leads to a single linear equation that is easy to solve. Once the variable is found, B age follows directly, and we can verify by checking the total and the relationships. Step-by-Step Solution: Step 1: Let the present age of C be c years. Step 2: Since B is twice as old as C, B present age is 2c years. Step 3: A is two years older than B, so A present age is 2c + 2 years. Step 4: The total of their ages is A + B + C = (2c + 2) + 2c + c, which simplifies to 5c + 2. Step 5: Given that the total is 27, we set 5c + 2 = 27 and solve for c to get c = 5 years. Step 6: Then B present age is 2c = 10 years, which is the required answer. Verification / Alternative check: Using the values we found, C is 5 years old, B is 10 years old, and A is 12 years old. Add them: 5 + 10 + 12 = 27, which matches the total given in the problem. Also check the relationships: B is twice C because 10 = 2 × 5, and A is two years older than B because 12 = 10 + 2. Both conditions are satisfied, so the solution is correct and consistent with all parts of the question. Why Other Options Are Wrong: Option 11 yrs: If B were 11, C would be 5.5 and the total would not come to 27, so this is not acceptable under the usual whole number age assumption. Option 12 yrs: This would give a different distribution of ages that does not match the total or the twice relationship exactly. Option 13 yrs and Option 9 yrs: Similar checks show that they produce sums or relations that are inconsistent with the given conditions, so they cannot be correct. Common Pitfalls: A typical mistake is to choose the wrong person for the variable or to forget that A is older than B by 2 years, not the other way around. Some learners also incorrectly add or subtract ages when setting up the sum. A clear strategy is to write each age in terms of the youngest person, sum them carefully, and double check that all relationships are respected. Drawing a quick age diagram can also help avoid confusion. Final Answer: The present age of person B is 10 years (that is, option 10 yrs).

Question 10

Three fifths of my current age is equal to five sixths of the current age of one of my cousins. My age ten years ago will be equal to his age four years from now. What is my current age in years?

Accepted Answer

Introduction / Context: This is a multi condition age puzzle involving fractions of ages and a comparison between past and future ages. The question tests your ability to handle rational relationships (fractions) as well as time shifts simultaneously. It is more challenging than simple ratio or difference based age problems because you must form and solve two equations with two unknowns, each equation containing fractional coefficients. Given Data / Assumptions: Three fifths of my current age equals five sixths of my cousin current age. My age ten years ago will be equal to my cousin age four years from now. We have to find my present age in years. Both people ages increase linearly and are assumed to be whole numbers in the final answer. Concept / Approach: This problem is best approached by using algebra. Define one variable for my current age and another for the cousin current age. The fraction statement gives one linear equation relating these variables. The comparison between my age ten years ago and cousin age four years hence gives another linear equation. Solving these two equations simultaneously yields the numerical value for my present age. Working carefully with fractions is crucial to avoid arithmetic errors. It is often helpful to clear denominators by multiplying both sides of the equation by a common multiple such as 30. Step-by-Step Solution: Step 1: Let my current age be M years and my cousin current age be C years. Step 2: From the fraction condition, (3/5) × M = (5/6) × C. Step 3: Multiply both sides by 30, a common multiple of 5 and 6, to avoid fractions. This gives 18M = 25C, so C = (18/25) × M. Step 4: The second condition says that my age ten years ago, M − 10, is equal to my cousin age four years from now, C + 4. Step 5: Substitute C = (18/25) × M into M − 10 = C + 4 and solve the resulting equation to obtain M = 50. Step 6: Therefore my current age is 50 years. Verification / Alternative check: Check the relationships using M = 50 years. Then my cousin age is C = (18/25) × 50 = 36 years. Now compute three fifths of my age: (3/5) × 50 = 30, and five sixths of my cousin age: (5/6) × 36 = 30. These are equal, so the first condition is satisfied. Next check the past and future condition: my age ten years ago was 40 years, and my cousin age four years from now will be 36 + 4 = 40 years. These also match, so both conditions hold exactly, confirming that 50 is the correct current age. Why Other Options Are Wrong: Option 60: If my age were 60, the cousin age from the first equation would not produce a match with the second condition when tested. Option 55: Substituting 55 in place of M fails to satisfy one or both equations, so it cannot be correct. Option 45: This value also leads to inconsistent results between the fraction condition and the age comparison condition. Option 40: If M is 40, three fifths of my age is 24, and this does not align with a cousin age that satisfies the second condition. Common Pitfalls: Students often mix up which age goes with which fraction or forget to align the past and future ages correctly. Another frequent mistake is to make algebraic slips when clearing denominators, for example by multiplying only one side or not multiplying every term. A good strategy is to write both equations clearly, choose a convenient common multiple to eliminate fractions, and only then proceed to substitution. Always verify both conditions at the end with the found ages to ensure the answer is fully consistent. Final Answer: My current age is 50 years.

Question 11

The sum of the present ages of a father and his son is 70 years. After 10 years, the son age will be exactly half of the father age. What are their present ages now?

Accepted Answer

Introduction / Context: This family based age problem involves a fixed sum of present ages and a simple relationship between their ages in the future. The condition that one person age will be exactly half of another person age after some years is a typical pattern in problems on ages. It helps to practice forming equations from such verbal statements and understanding how age relationships evolve over time. Given Data / Assumptions: The sum of the present ages of a father and his son is 70 years. After 10 years, the son age will be exactly half the age of the father at that time. We need to find their current ages. Ages grow in a normal way, so both father and son age by 10 years over the period. Concept / Approach: Let the father age and the son age be two variables. The first statement gives a simple sum equation. The second statement gives a proportional relationship between their future ages. By expressing the future ages in terms of the current ones and using the half relationship, we obtain a second equation. Solving the two linear equations together yields the present ages. This is a standard two variable, two equation algebra problem derived from an age context. Step-by-Step Solution: Step 1: Let the father present age be F years and the son present age be S years. Step 2: From the sum condition, F + S = 70. Step 3: After 10 years, the father age will be F + 10 and the son age will be S + 10. Step 4: The future condition says S + 10 is half of F + 10, so S + 10 = (F + 10) / 2. Step 5: Use these two equations to solve for F and S. You obtain F = 50 years and S = 20 years. Step 6: Thus the present ages are 50 years for the father and 20 years for the son. Verification / Alternative check: First verify the sum: 50 + 20 = 70 years, which matches the given total. After 10 years, the father will be 60 years old and the son will be 30 years old. In that future scenario, the son age 30 is exactly half of the father age 60. Both conditions are satisfied perfectly, so the ages 50 years and 20 years are correct and consistent with the problem statement. Why Other Options Are Wrong: Option 45 years, 25 years: The sum is 70, but after 10 years the ages will be 55 and 35, and 35 is not half of 55. Option 47 years, 23 years: The sum is 70, but after 10 years they will be 57 and 33, and 33 is not half of 57. Option 50 years, 25 years: After 10 years the ages would be 60 and 35, and 35 is not half of 60. Option 40 years, 30 years: The sum is 70, but after 10 years they will be 50 and 40, and 40 is not half of 50. Common Pitfalls: A frequent mistake is to misread the condition and think that the son is half the father age at present rather than after 10 years. Another common error is to forget to add 10 years to both ages when forming the half equation. Always check that time shifts apply equally to all people involved and that you use future ages when the statement clearly refers to a future time. Revisiting the wording carefully reduces such misunderstandings. Final Answer: The present ages are 50 years for the father and 20 years for the son.

Question 12

The present ages of Sunil and Anil are in the ratio 8 : 7. After 6 years, the ratio of their ages will be 19 : 17. What is the difference between their present ages in years?

Accepted Answer

Introduction / Context: This question is another example of a two time ratio problem on ages. It provides the current ratio of ages and the ratio after a certain number of years. From this information you have to deduce the actual ages and then compute their difference. Problems like this test both algebraic manipulation and understanding of how adding the same number to both terms of a ratio affects that ratio. Given Data / Assumptions: Present ages of Sunil and Anil are in the ratio 8 : 7. After 6 years, their ages will be in the ratio 19 : 17. We are required to find the difference between their present ages. Both persons age normally by 6 years over the given period. Concept / Approach: The standard approach is to represent the present ages as multiples of a common variable, using the given ratio. Then we write expressions for their ages after 6 years and equate the resulting ratio to the second one. This gives a linear equation in the variable. Solving it yields the variable, from which we can compute the actual ages and their difference. This method relies on the fact that ratios provide relative information which becomes absolute once one more equation is known. Step-by-Step Solution: Step 1: Let the present ages of Sunil and Anil be 8k and 7k years respectively. Step 2: After 6 years, their ages will be 8k + 6 and 7k + 6 years. Step 3: The future ratio condition says (8k + 6) : (7k + 6) = 19 : 17. Step 4: Form the equation (8k + 6) / (7k + 6) = 19 / 17 and solve for k. Step 5: Solving gives k = 4, so the present ages are 32 years for Sunil and 28 years for Anil. Step 6: The difference between their present ages is 32 − 28 = 4 years. Verification / Alternative check: Check the ratios with the found ages. The present ratio 32 : 28 simplifies to 8 : 7, which matches the given ratio. After 6 years, the ages will be 38 and 34, and the ratio 38 : 34 reduces to 19 : 17, which matches the future ratio. Since both ratios come out correctly, the difference of 4 years is confirmed as accurate and the solution is consistent with all conditions. Why Other Options Are Wrong: Option 10 years, 6 years, and 8 years: These larger differences would generate present ages that do not fit both ratios at the same time. Testing these differences with suitable pairs fails either the present or future ratio condition. Option 2 years: This difference is too small; if you try to construct ages with a 2 year gap and ratio 8 : 7, the arithmetic does not work correctly. Common Pitfalls: A common error is to forget to add 6 years to both ages in the future ratio or to write the equation with the ratios reversed. Some learners also try to guess ages instead of systematically solving the algebra, which can be time consuming and prone to mistakes. Writing the ratio equation clearly, cross multiplying carefully, and checking both ratios at the end ensures a reliable solution. Final Answer: The difference between the present ages of Sunil and Anil is 4 years.

Question 13

Nine years later, the age of B will be equal to the present age of A. The sum of A age 3 years later and B age 4 years ago is 76. If C is currently half of the present age of B, then what will be C age in years after 10 years?

Accepted Answer

Introduction / Context: This is a multi person age problem involving three individuals A, B and C. Two separate conditions relate the ages of A and B at different times, and a third condition defines C age in terms of B present age. The question then asks for C age after 10 years. Such questions test your ability to combine multiple time shifted age relationships and then propagate the result to a third person. Given Data / Assumptions: Nine years later, B age will be equal to the present age of A. The sum of A age 3 years later and B age 4 years ago is 76. C is currently half of B present age. We are required to find C age after 10 years. All ages change linearly and are measured in full years. Concept / Approach: We set up variables for the present ages of A and B. The first condition gives a direct equation linking A and B by comparing B future age to A present age. The second condition provides a second equation that involves both A and B again but now in terms of future and past ages. Solving this system gives the present values of A and B. Then, using the relation that C is half of B present age, we can find C now and then add 10 years to get C future age. This method follows a simple algebraic framework but requires careful attention to time shifts. Step-by-Step Solution: Step 1: Let the present ages of A and B be a and b years respectively. Step 2: Nine years later, B age will be b + 9, and this is equal to the present age of A, so a = b + 9. Step 3: A age 3 years later is a + 3 and B age 4 years ago is b − 4. Their sum is given as 76, so (a + 3) + (b − 4) = 76. Step 4: Simplify the second equation to a + b − 1 = 76, so a + b = 77. Step 5: Solve the system a = b + 9 and a + b = 77. This gives a = 43 years and b = 34 years. Step 6: C is half of B present age, so C now is 34 ÷ 2 = 17 years. After 10 years, C age will be 17 + 10 = 27 years. Verification / Alternative check: Verify the conditions with a = 43 and b = 34. Nine years later, B will be 34 + 9 = 43 years, equal to A present age, satisfying the first condition. Three years later, A will be 46 and four years ago, B was 34 − 4 = 30. Their sum is 46 + 30 = 76, which matches the second condition. Since C is half of 34, C is 17 now and will be 27 after 10 years. All parts of the problem are consistent, confirming the correctness of the solution. Why Other Options Are Wrong: Option 32, 36, 31, and 29: All of these values assume incorrect present ages for A and B when traced back into the equations. Substituting them leads to sums or equalities that do not match the stated conditions, so they cannot be right for C age after 10 years. Common Pitfalls: It is easy to mix up whether an age is present, past, or future. Many learners mistakenly set a = b − 9 instead of a = b + 9 or incorrectly handle the sum involving future and past ages. A good practice is to sketch a small timeline for each person, label present, future, and past points, and only then translate the statements into equations. This reduces confusion and makes the algebra much more reliable. Final Answer: C age after 10 years will be 27 years.

Question 14

A mother is five times older than her daughter at present. After 5 years, she will be three times older than her daughter. What is the mother present age in years?

Accepted Answer

Introduction / Context: This is a standard mother daughter age relationship problem. At the present time, one age is a multiple of the other, and in the future the same relation changes to a different multiple. The question asks for the present age of the mother. Such problems are common in aptitude exams and help strengthen skills in handling linear equations with simple multiples and a fixed time shift. Given Data / Assumptions: At present, the mother is five times as old as her daughter. After 5 years, the mother will be three times as old as her daughter. We need to find the current age of the mother. Both ages increase by 5 years over the given period. Concept / Approach: We use a variable for the daughter present age and express the mother present age as a multiple of that variable. Then we form expressions for their ages after 5 years and use the future three times relationship to create an equation. Solving this linear equation gives the daughter age, and multiplying appropriately gives the mother age. This method is very direct and highlights the importance of reading the word times as a multiplier in the algebraic equation. Step-by-Step Solution: Step 1: Let the present age of the daughter be x years. Step 2: The mother is five times older, so her present age is 5x years. Step 3: After 5 years, the daughter will be x + 5 years old and the mother will be 5x + 5 years old. Step 4: The condition after 5 years says 5x + 5 is three times x + 5, so 5x + 5 = 3 × (x + 5). Step 5: Solve this linear equation to get x = 5 years. Therefore, the mother present age is 5x = 25 years. Step 6: Thus, the required present age of the mother is 25 years. Verification / Alternative check: Using the found ages, the daughter is 5 years old and the mother is 25 years old at present. This clearly matches the statement that the mother is five times older than her daughter now, because 25 = 5 × 5. After 5 years, their ages will be 10 and 30 respectively. At that time, 30 is three times 10, confirming the second condition. Both conditions are satisfied, so the computed mother age is correct. Why Other Options Are Wrong: Option 20 years: If the mother were 20, the daughter present age would have to be 4, and after 5 years they would be 25 and 9, which does not give a three times relation. Option 22 years and 29 years: These values do not satisfy both the five times and three times conditions when you attempt to back calculate the daughter age. Option 30 years: This would give a different ratio now and in the future which does not align with the problem statements. Common Pitfalls: One common confusion is the phrase five times older, which some learners misread as five years older. Here it clearly means five times the daughter age. Another mistake is forgetting to add 5 years to both ages when using the future condition. Carefully distinguishing multiples from differences and tracking the time shift prevent such errors. Final Answer: The mother present age is 25 years.

Question 15

The average age of eight teachers in a school is 40 years. One teacher among them dies at the age of 55 years and another teacher whose age is 39 years joins the staff. What is the new average age in years of the teachers in the school now?

Accepted Answer

Introduction / Context: This problem combines the concept of average with a change in the group membership. One teacher leaves (by death) and another teacher joins with a different age. You are asked to find the new average age of the group. Such questions are common in aptitude tests and are useful practice for understanding how averages are affected when one value is removed and another is added. Given Data / Assumptions: There are eight teachers initially. The average age of these eight teachers is 40 years. One teacher dies at the age of 55 years. A new teacher aged 39 years joins the group. The number of teachers after the change remains eight. We must find the new average age of the teachers. Concept / Approach: Average age is the total of all ages divided by the number of people. Initially, we can find the total age of the eight teachers by multiplying the average by the number of teachers. When one teacher leaves, we subtract that age from the total. When a new teacher joins, we add the new age. The number of teachers remains the same, so the new average is the adjusted total divided by the same number of teachers. This method is simpler and more reliable than trying to track each individual age. Step-by-Step Solution: Step 1: Compute the initial total age of the eight teachers as 8 × 40 = 320 years. Step 2: One teacher aged 55 leaves, so subtract 55 from 320 to get 265 years as the total age of the remaining seven teachers. Step 3: A new teacher aged 39 joins, so add 39 to 265 to get a new total of 304 years. Step 4: There are still eight teachers in the group, so the new average age is 304 ÷ 8 = 38 years. Step 5: Thus the new average age of the teachers is 38 years. Verification / Alternative check: We can also reason about the change in average without computing every detail. The teacher who left was 55 years old, which is 15 years above the original average of 40. The teacher who joined is 39 years old, which is 1 year below 40. Effectively, we removed an age that was 15 above the old average and added an age that is 1 below it, a net change of 16 years less in total over 8 people. A decrease of 16 in total divided by 8 teachers gives a decrease of 2 in the average, moving it from 40 down to 38, which matches our calculation. Why Other Options Are Wrong: Option 35 and 36: These would require a larger drop in the total age than what actually occurs when 55 is replaced by 39. Option 39: This would imply almost no significant effect from replacing a 55 year old teacher with a 39 year old one, which is not correct. Option 40: This is the original average and does not reflect the change in the staff composition. Common Pitfalls: A common mistake is to forget that the number of teachers stays the same after one leaves and another joins, leading to an incorrect divisor when calculating the new average. Another error is to add and subtract the ages incorrectly, especially when doing mental arithmetic. Writing down each step clearly and double checking the computed totals will help avoid such calculation errors. Final Answer: The new average age of the teachers is 38 years.

Question 16

Five years hence, the ratio of the ages of A and B will be 7 : 5 and the difference between their ages at that time will be 4 years. What are the present ages in years of A and B respectively?

Accepted Answer

Introduction / Context: This age problem describes the ratio of two people ages in the future and also provides the difference between their ages at that time. From this future information, you must work backward to their present ages. Such questions reinforce understanding that the difference in ages remains constant over time, while ratios can change, and they provide good practice with simple ratio arithmetic. Given Data / Assumptions: Five years hence, the ratio of the ages of A and B will be 7 : 5. At that same future time, the difference between their ages will be 4 years. We need to find their present ages, A and B, in years. Age difference between two people stays the same at all times. Concept / Approach: Let the ages of A and B after 5 years be 7k and 5k respectively, based on the ratio. The difference between these future ages is 2k, which is given as 4 years, allowing us to determine k. Once we know the future ages as exact numbers, we subtract 5 years from each to obtain the present ages. This approach combines basic ratio manipulation with the idea that moving forward or backward by the same number of years affects both individuals equally. Step-by-Step Solution: Step 1: Let A age after 5 years be 7k years and B age after 5 years be 5k years. Step 2: The difference between their ages after 5 years is 7k − 5k = 2k, and this difference is given as 4 years. Step 3: Set 2k = 4 and solve to find k = 2. Step 4: Then A age after 5 years is 7 × 2 = 14 years and B age after 5 years is 5 × 2 = 10 years. Step 5: To find present ages, subtract 5 years from these values. So A present age is 14 − 5 = 9 years and B present age is 10 − 5 = 5 years. Step 6: Therefore, the present ages of A and B respectively are 9 years and 5 years. Verification / Alternative check: Check both conditions using the present ages 9 and 5. After 5 years, A will be 14 and B will be 10. Their ratio 14 : 10 simplifies to 7 : 5, matching the given ratio. The difference between 14 and 10 is exactly 4 years, matching the stated difference. Since both conditions are satisfied, the present ages 9 and 5 are confirmed as correct. Why Other Options Are Wrong: Option 5, 9: This reverses the correct order of A and B and does not agree with the ratio when considered as A first, B second. Option 6, 5: If these were the present ages, then after 5 years they would be 11 and 10, whose ratio is not 7 : 5 and difference is only 1 year. Option 9, 6 and Option 10, 6: These pairs fail either the future ratio or the future difference condition when checked after adding 5 years to both ages. Common Pitfalls: Some learners forget that the age difference remains the same at all times and try to recalculate it incorrectly. Others misinterpret the phrase five years hence and mistakenly subtract 5 rather than add 5 when working out the future ages. Using a clear timeline and keeping track of which ages belong to the present and which to the future helps avoid confusion. Final Answer: The present ages of A and B respectively are 9 years and 5 years.

Question 17

The average age of a class of 6 girls is x years. Four new girls join the class with ages x − 2, x + 2, x + 4 and x + 6 years. What is the new average age in years of the class?

Accepted Answer

Introduction / Context: This question deals with average age and how it changes when new members join a group. The original group has a symbolic average of x years rather than a specific number, and the new members have ages given in terms of x as well. The task is to compute the new average in algebraic form. Problems like this are helpful for understanding averages in a general algebraic setting, which is useful for many aptitude and math examinations. Given Data / Assumptions: The class initially has 6 girls, and their average age is x years. The total age of these 6 girls is therefore 6x years. Four new girls join with ages x − 2, x + 2, x + 4 and x + 6 years. We need to find the new average age of all 10 girls together. Concept / Approach: Average age is calculated as total age divided by the number of people. The initial total age can be obtained by multiplying the average by the number of girls. After new members join, the total age becomes the sum of the original total plus the ages of the new girls. The new average is the new total divided by the new group size. Since everything is expressed in terms of x, we carry out the algebra carefully and simplify the expression to a neat form. Step-by-Step Solution: Step 1: Compute the initial total age of the 6 girls as 6 × x = 6x years. Step 2: Add the ages of the four new girls: (x − 2) + (x + 2) + (x + 4) + (x + 6). Step 3: Simplify this sum to get 4x + 10 years. Step 4: The new total age of all 10 girls is 6x + (4x + 10) = 10x + 10 years. Step 5: The new number of girls is 10, so the new average age is (10x + 10) ÷ 10 = x + 1. Step 6: Therefore, the new average age of the class is x + 1 years. Verification / Alternative check: To confirm, choose a simple value for x, for example x = 10. Initially, the total age of 6 girls is 60 and the average is 10. The new girls have ages 8, 12, 14 and 16, whose sum is 50. The new total becomes 60 + 50 = 110 and the new average is 110 ÷ 10 = 11. This is x + 1 when x is 10, confirming that the formula x + 1 is consistent for this test case. Because the relationship is linear and the computation was symbolic, the result holds for all valid values of x. Why Other Options Are Wrong: Option x + 2: This would require a new total age of 10x + 20, which does not match the algebraic sum of the actual ages. Option 2.5x: This grows too rapidly with x compared to the correct linear expression and does not fit simple test values. Option x + 2.5: This suggests an extra 1.5 years added compared to the true new average, and fails when checked with sample values of x. Option x: This would mean no change in average despite adding older and younger girls, which is inconsistent with the computed total. Common Pitfalls: Learners sometimes forget to include all terms correctly when summing the new girls ages or make algebraic slips like misadding constants. Another common mistake is to divide by the wrong number of girls, for example by 6 instead of 10. Keeping track of the group size after the join and carefully simplifying the algebraic expressions step by step prevents such errors. Final Answer: The new average age of the class is x + 1 years.

Question 18

The ratio of the present ages of Aman and Ankit is 2 : 1 and the sum of their present ages is 72 years. What will be Aman age in years after 6 years from now?

Accepted Answer

Introduction / Context: This problem is a straightforward ratio and sum based age question. The present ages of two people are in a given ratio, and their sum is known. From this data, you must determine one person age after a few years. Such questions reinforce the link between ratios, total sums, and future ages, and they are frequently tested in aptitude exams. Given Data / Assumptions: The ratio of the present ages of Aman and Ankit is 2 : 1. The sum of their present ages is 72 years. We need to find Aman age after 6 years. Both ages increase normally by 6 years over the given period. Concept / Approach: Express the present ages of Aman and Ankit as 2k and 1k respectively using the given ratio. Then use the given sum to compute k. Once k is known, Aman present age can be obtained, and adding 6 years gives Aman age after 6 years. This is a standard use of ratio and sum information to convert relative ages into actual ages. Step-by-Step Solution: Step 1: Let Aman present age be 2k years and Ankit present age be k years. Step 2: From the sum condition, 2k + k = 72, so 3k = 72. Step 3: Solving 3k = 72 gives k = 24. Step 4: Aman present age is 2k = 2 × 24 = 48 years. Step 5: After 6 years, Aman age will be 48 + 6 = 54 years. Step 6: Therefore, Aman age after 6 years will be 54 years. Verification / Alternative check: Once we have Aman present age as 48 years, Ankit present age is 24 years, because the ratio is 2 : 1. The sum 48 + 24 = 72 years matches the total given in the question, confirming that the value of k is correct. After 6 years, their ages will be 54 and 30 respectively, and although the ratio changes, the question only asks for Aman age, which we have accurately determined as 54 years. Why Other Options Are Wrong: Option 30 and 48: These correspond to present ages or incorrect future ages and do not reflect Aman age after 6 years when solved correctly. Option 52 and 50: These values do not match the linear increase from the correct present age of 48 when 6 years are added, nor do they agree with any consistent ratio setup. Common Pitfalls: Some learners mistakenly divide 72 by 2 instead of 3, or assign the ratio parts incorrectly, for example switching the ages of Aman and Ankit. It is important to clearly label the ratio and carefully use the sum to find the correct value of the common factor. Double checking that the sum of the derived ages matches the given total helps confirm that there are no basic errors. Final Answer: Aman age after 6 years will be 54 years.

Question 19

The ratio of the present ages of Ranjini and Shahid is 5 : 4. After 13 years, the ratio of their ages will be 6 : 5. What is Ranjini present age in years?

Accepted Answer

Introduction / Context: This is a typical two time ratio problem on ages involving Ranjini and Shahid. The present ratio of their ages is given, and another ratio is given for their ages after a fixed period of 13 years. Your task is to find Ranjini present age. Such problems test your skill in setting up algebraic expressions for ages at different times and solving the resulting equations. Given Data / Assumptions: The present age ratio of Ranjini to Shahid is 5 : 4. After 13 years, their age ratio will be 6 : 5. We have to determine Ranjini present age. Both ages increase linearly by 13 years over the period. Concept / Approach: Let the present ages be 5k and 4k for Ranjini and Shahid respectively. After 13 years, their ages become 5k + 13 and 4k + 13. The future ratio condition gives a fraction equation involving k. Solving this equation yields the value of k and hence the actual ages. The method uses basic algebra and the idea that adding a fixed number to both terms of a ratio changes the ratio in a predictable way. Step-by-Step Solution: Step 1: Let Ranjini present age be 5k years and Shahid present age be 4k years. Step 2: After 13 years, their ages will be 5k + 13 and 4k + 13 years. Step 3: According to the question, (5k + 13) : (4k + 13) = 6 : 5. Step 4: Convert this into the equation (5k + 13) / (4k + 13) = 6 / 5 and solve for k. Step 5: Solving the equation gives k = 13. Thus, Ranjini present age is 5k = 5 × 13 = 65 years. Step 6: Therefore, the required present age of Ranjini is 65 years. Verification / Alternative check: Check using Ranjini age 65 and Shahid age 52 (since 4 × 13 = 52). Their present ratio is 65 : 52, which simplifies to 5 : 4 by dividing both numbers by 13. After 13 years, their ages will be 78 and 65 respectively. The ratio 78 : 65 simplifies to 6 : 5 by dividing by 13 again. Both ratio conditions are satisfied, confirming that 65 is Ranjini correct present age. Why Other Options Are Wrong: Option 52 and 60: These do not maintain both the present and future ratios when you back calculate Shahid age and check the conditions. Option 32 and 40: These values are too small and lead to future ages and ratios that do not match the given 6 : 5 relationship after 13 years. Common Pitfalls: Learners sometimes swap the roles of Ranjini and Shahid when assigning the ratio parts, which leads to incorrect equations. Another common mistake is to forget to add 13 years to both ages before forming the second ratio. Writing the ratio equation carefully and double checking which term corresponds to which person helps prevent these errors. Final Answer: Ranjini present age is 65 years.

Question 20

The ratio of A age to B age is 4 : 3. A will be 26 years old after 6 years. What is the present age of B in years?

Accepted Answer

Introduction / Context: This is a simple ratio and future age based problem on ages. The current ratio of two ages is given, and a future value for one person age is specified. You must find the current age of the other person. Such questions are excellent practice for connecting present and future ages and for using ratios to derive actual numbers. Given Data / Assumptions: The ratio of the present ages of A and B is 4 : 3. A will be 26 years old after 6 years. We need to find B present age. Both A and B age normally by 6 years over the period. Concept / Approach: First determine A present age from the given future age information. Then use the ratio to find B age. Since the ratio 4 : 3 relates the present ages, we can set up a proportion using A present age and solve for B. This avoids the need for introducing an extra variable for the ratio. The method is direct and relies on basic proportional reasoning. Step-by-Step Solution: Step 1: A will be 26 years old after 6 years, so A present age is 26 − 6 = 20 years. Step 2: The ratio of the present ages A : B is 4 : 3, meaning A / B = 4 / 3. Step 3: Substitute A = 20 into the ratio to get 20 / B = 4 / 3. Step 4: Solve this proportion to get B = (3 / 4) × 20 = 15 years. Step 5: Hence, the present age of B is 15 years. Verification / Alternative check: Check the ratio with the found ages. If A is 20 and B is 15, the ratio 20 : 15 simplifies to 4 : 3 when both numbers are divided by 5, which matches the given ratio. Also, after 6 years, A will indeed be 26 years old, which is consistent with the given future age. Therefore, the solution is correct and satisfies all the conditions of the question. Why Other Options Are Wrong: Option 12 years: If B were 12, the ratio would be 20 : 12, which simplifies to 5 : 3, not 4 : 3. Option 21 years: This gives a ratio of 20 : 21, which is less than 1 and does not simplify to 4 : 3. Option 13 years and 18 years: These values also do not produce the correct 4 : 3 ratio when paired with A present age of 20 years. Common Pitfalls: Learners sometimes forget to subtract the 6 years to find A present age or misapply the ratio by writing 3 : 4 instead of 4 : 3. Another common problem is inverting the fraction incorrectly when solving the proportion. Careful writing of the ratio and systematic cross multiplication help avoid these algebraic mistakes. Final Answer: The present age of B is 15 years.

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