Question 1

Fresh grapes contain 60% water by weight, while dry grapes contain 40% water by weight. If you start with 60 kg of fresh grapes, how many kilograms of dry grapes will you obtain after drying (assuming only water is removed)?

Accepted Answer

Introduction / Context: This is a classic percentage and mixture style problem that uses the concept of constant solids. When fresh grapes are dried, water is removed but the solid portion remains the same. By tracking the solid part before and after drying, we can determine the final weight of the dry grapes. Questions of this type are frequently asked to test logical reasoning with percentages and composition. Given Data / Assumptions: Weight of fresh grapes = 60 kg. Fresh grapes contain 60% water and therefore 40% solids. Dry grapes contain 40% water and therefore 60% solids. Only water is removed during drying and the amount of solid matter remains constant. Concept / Approach: The key idea is that solid content does not change during drying. First, calculate the amount of solid substance in the fresh grapes. Next, assume that the same amount of solid substance is present in the dry grapes, but it now constitutes 60% of the total weight of the dry grapes. Using this relationship, set up an equation for the unknown final weight and solve it. Step-by-Step Solution: Step 1: Fresh grapes are 60% water and 40% solids.Step 2: Solid mass in fresh grapes = 40% of 60 kg = (40 / 100) * 60 = 24 kg.Step 3: In dry grapes, water is 40%, so solids are 60% of the final weight.Step 4: Let the final weight of dry grapes be W kg.Step 5: Since solids remain the same, 60% of W equals 24 kg.That is, (60 / 100) * W = 24.Step 6: Solve for W: W = 24 * 100 / 60 = 24 * (5 / 3) = 40 kg. Verification / Alternative check: Check the composition of dry grapes at the final weight. If the final weight is 40 kg and solids are 60%, then solids = 0.60 * 40 = 24 kg, and water = 16 kg. This matches the solid mass we computed from the fresh grapes, so the mass balance is correct. Why Other Options Are Wrong: 25 kg and 30 kg give too little solid mass if you apply the 60% solids condition, which contradicts the original 24 kg of solids. 35 kg also fails to deliver exactly 24 kg solids when multiplied by 60%, so it cannot be correct. 32 kg is another distractor that does not satisfy the equality of solid mass before and after drying. Common Pitfalls: A common mistake is to think that water content alone changes linearly and to subtract percentages incorrectly. Another frequent error is to treat the percentage values as if they apply to the same total weight, rather than recognizing that fresh and dry grapes have different total weights. Always focus on the invariant quantity, which is the solid part, and then express that as a percentage of the new total weight to find the final answer. Final Answer: From 60 kg of fresh grapes, you will obtain 40 kg of dry grapes.

Question 2

Lucky started working two years ago. At that time her starting salary was exactly half of Karthik salary. Since then, both Lucky and Karthik have received a yearly salary increase of 10% each. What percentage of Karthik current salary is equal to Lu…

Accepted Answer

Introduction / Context: This question combines percentage growth with ratio comparison. Both employees receive the same percentage raise each year, but their starting salaries are different. The problem asks you to compare their current salaries after two years of 10% annual increments. Understanding how equal percentage changes affect ratios is essential for solving many salary, population, and investment problems. Given Data / Assumptions: Let Karthik starting salary be K rupees. Lucky starting salary is half of that, that is K / 2 rupees. Both Lucky and Karthik receive a 10% salary increase every year. We are dealing with a period of two years. We need the ratio Lucky current salary ÷ Karthik current salary expressed as a percentage. Concept / Approach: If two quantities are increased or decreased by the same percentage, their ratio remains unchanged. Here both Lucky and Karthik receive 10% raises in each of the two years, so their salaries are each multiplied by the same factor (1.1 twice). Therefore, even after the raises, Lucky salary will remain exactly half of Karthik salary. After recognizing this, we simply convert the ratio to a percentage. Step-by-Step Solution: Step 1: Let Karthik initial salary be K.Step 2: Lucky initial salary = K / 2.Step 3: After one year, both salaries are multiplied by 1.1 (since 10% increase means multiply by 1.10).After two years, each salary is multiplied by (1.1)^2 = 1.21.Step 4: Karthik current salary = K * 1.21.Step 5: Lucky current salary = (K / 2) * 1.21 = 0.5 * K * 1.21.Step 6: Ratio Lucky current salary to Karthik current salary = (0.5 * K * 1.21) / (K * 1.21) = 0.5.Step 7: Convert 0.5 to a percentage: 0.5 * 100 = 50%. Verification / Alternative check: You can test with actual numbers. Suppose Karthik started at Rs. 20,000 and Lucky at Rs. 10,000. After two years, both get 10% raises each year. Karthik salary becomes 20,000 * 1.21 = 24,200. Lucky salary becomes 10,000 * 1.21 = 12,100. Now 12,100 is exactly half of 24,200, confirming the 50% ratio. Why Other Options Are Wrong: 75%, 35%, and 60% assume that equal percentage increases can change the original half relationship, which is not correct. 22.5% is far too small and does not relate to the original ratio of 1 : 2. Common Pitfalls: Many candidates try to compute each salary year by year using absolute amounts and then divide, which is fine but more time consuming. Others mistakenly think that because both salaries grow at the same rate, their difference remains constant while the ratio changes. In percentage growth problems, remember that equal percentage changes preserve the original ratio even though the absolute difference between the two salaries may increase. Final Answer: Lucky current salary is 50% of Karthik current salary.

Question 3

What is 15% of 32?

Accepted Answer

Introduction / Context: This is a direct percentage calculation, designed to test whether you can quickly convert a percentage into a fraction or decimal and multiply it with a given number. Such simple questions form the foundation for more complex percentage and ratio problems in aptitude tests. Given Data / Assumptions: We need to find 15% of 32. Percentage is always calculated as (percentage / 100) times the base value. Concept / Approach: To calculate x% of a number N, use the formula: x% of N = (x / 100) * N. Here, x = 15 and N = 32. We convert 15% into a fraction or decimal and multiply by 32 to get the required value. It is often helpful to simplify the fraction 15 / 100 to 3 / 20 before multiplying, which makes the calculation easier. Step-by-Step Solution: Step 1: Write 15% as a fraction: 15% = 15 / 100.Step 2: Simplify 15 / 100 by dividing numerator and denominator by 5, giving 3 / 20.Step 3: Compute 3 / 20 of 32: (3 / 20) * 32.Step 4: 32 / 20 = 1.6, so (3 / 20) * 32 = 3 * 1.6 = 4.8.Step 5: Therefore 15% of 32 equals 4.8. Verification / Alternative check: You can also use decimal conversion directly: 15% = 0.15, so 0.15 * 32 = 4.8. This matches the earlier result and confirms that 4.8 is correct. Why Other Options Are Wrong: 3.6 corresponds roughly to 11.25% of 32, not 15%. 5.2 and 5.8 are larger than the correct value and do not correspond to any nice simple percentage of 32. 4.2 is another distractor that does not match 15% of 32. Common Pitfalls: Common mistakes include dividing 32 by 15 instead of multiplying by 15 / 100, or misplacing the decimal when converting from percent to decimal. Some test takers also confuse the meaning of percent and attempt arithmetic without converting to fraction or decimal. Always remember that x% means x parts out of 100 and use (x / 100) * number as your standard method. Final Answer: 15% of 32 is 4.8.

Question 4

What is 5% of 400000?

Accepted Answer

Introduction / Context: This question tests your ability to quickly compute a simple percentage of a large number. Although the number 400000 looks big, the calculation is straightforward once you remember how to interpret percentages. Such quick mental calculations are very helpful in competitive exams and day to day financial decisions. Given Data / Assumptions: We need to find 5% of 400000. We interpret 400000 as four lakh in the Indian numbering system. Concept / Approach: The standard formula for percentage is: x% of N = (x / 100) * N. Here x = 5 and N = 400000. Simplifying 5 / 100 gives 1 / 20, which makes the multiplication with 400000 very easy to handle. This method avoids dealing with long decimals and keeps the calculation clear and exact. Step-by-Step Solution: Step 1: Express 5% as a fraction: 5% = 5 / 100.Step 2: Simplify 5 / 100 = 1 / 20.Step 3: Compute (1 / 20) of 400000.400000 / 20 = 400000 / (2 * 10) = 200000 / 10 = 20000.Step 4: Therefore, 5% of 400000 = 20000. Verification / Alternative check: Alternatively, convert 5% to decimal: 5% = 0.05. Then multiply: 0.05 * 400000 = 5 * 400000 / 100 = 2000000 / 100 = 20000. This matches the earlier computation, confirming the correctness of the result. Why Other Options Are Wrong: 4000 is only 1% of 400000, not 5%. 16000 and 8000 are arbitrary smaller values that do not match 5% of 400000. 10000 corresponds to 2.5% of 400000, which is half of the required percentage. Common Pitfalls: Some candidates mistakenly move the decimal point incorrectly or misinterpret 5% as 0.5 instead of 0.05. Others divide by 5 instead of multiplying by 5 / 100. To avoid such errors, always carefully convert percentage to fraction or decimal first and then perform the multiplication using simple steps or factorization tricks like cancelling zeros and dividing systematically. Final Answer: 5% of 400000 is 20000.

Question 5

In an examination a candidate scored 30% of the total marks and failed by 30 marks. If the pass mark is 60% of the total marks, what is the maximum possible total mark for the examination?

Accepted Answer

Introduction / Context: This examination style problem involves interpreting percentages of total marks and understanding how many marks a candidate falls short by. With a known failure margin in marks and two given percentage levels, you can work backwards to determine the total marks in the exam. This pattern is very popular in competitive tests for building comfort with percentages and algebraic reasoning. Given Data / Assumptions: The candidate scored 30% of the maximum marks. The candidate failed and was 30 marks short of the pass mark. The pass mark is 60% of the total marks. We need to find the maximum total marks in the examination. Concept / Approach: Let the maximum marks be M. Then the candidate mark is 30% of M, and the passing mark is 60% of M. The difference between these two is given as 30 marks. In symbols: 60% of M − 30% of M = 30. Use percent to decimal conversion and solve the resulting linear equation to get M. This is a direct application of basic algebra combined with percentage calculations. Step-by-Step Solution: Step 1: Let maximum marks be M.Step 2: Candidate marks = 30% of M = (30 / 100) * M = 0.30 * M.Step 3: Pass marks = 60% of M = (60 / 100) * M = 0.60 * M.Step 4: Given that the candidate failed by 30 marks, so 0.60 * M − 0.30 * M = 30.Step 5: Left side simplifies to (0.60 − 0.30) * M = 0.30 * M.Step 6: Therefore 0.30 * M = 30.Step 7: Solve for M: M = 30 / 0.30 = 30 * (100 / 30) = 100. Verification / Alternative check: If maximum marks are 100, then candidate marks = 30% of 100 = 30. Pass marks = 60% of 100 = 60. The difference between pass marks and candidate marks is 60 − 30 = 30 marks, exactly as stated in the question. Hence the total marks of 100 are fully consistent. Why Other Options Are Wrong: If M were 300, then 30% of 300 = 90 and 60% of 300 = 180, difference 90 marks, not 30. For 450 or 600, the differences between 30% and 60% would be very large (135 and 180 respectively), again not 30. 750 would give an even larger difference. None of these values satisfy the equation 0.30 * M = 30. Common Pitfalls: Some students confuse the meaning of failing by 30 marks and incorrectly treat 30 as a percentage instead of a number of marks. Others mix up which percentage corresponds to pass and which to the candidate score. A clear variable definition, consistent use of the percentage formula, and careful reading of the phrase "failed by 30 marks" are crucial for solving this type of question correctly. Final Answer: The maximum total marks in the examination are 100.

Question 6

In a village, 5/9 of the population are females and 30% of these females are married. What percentage of the total male population in the village are unmarried?

Accepted Answer

Introduction / Context: This problem mixes ratios and percentages in a population setting. The key idea is to interpret the fractions of females and males, then use the percentage of married females to infer how many males are married, assuming each married female is paired with one married male. Finally, we compute the share of unmarried males as a percentage of the total male population. Given Data / Assumptions: Females constitute 5/9 of the total population. Therefore males constitute the remaining 4/9 of the total population. 30% of the females are married. Each married female is married to exactly one male, and there are no polygamous or other special cases. We need the percentage of unmarried males in the total male population. Concept / Approach: It is convenient to assume the total population is 9 units so that 5 units are females and 4 units are males. Then 30% of the females are married, giving a fixed number of married females. Under the assumption of monogamous couples, the number of married males must equal the number of married females. Subtracting married males from the total male population gives unmarried males. Finally, we convert that number into a percentage of all males. Step-by-Step Solution: Step 1: Assume total population = 9x for some positive x.Step 2: Females = (5 / 9) * 9x = 5x and males = (4 / 9) * 9x = 4x.Step 3: 30% of females are married.Married females = 30% of 5x = (30 / 100) * 5x = 1.5x.Step 4: Under one to one marriage assumption, married males = 1.5x.Step 5: Unmarried males = total males − married males = 4x − 1.5x = 2.5x.Step 6: Percentage of unmarried males among total males = (2.5x / 4x) * 100.The x cancels out giving (2.5 / 4) * 100 = 0.625 * 100 = 62.5%. Verification / Alternative check: Take a concrete example: let x = 2 so that total population is 18. Then females = 10, males = 8. Married females = 30% of 10 = 3, married males = 3, so unmarried males = 8 − 3 = 5. Therefore the percentage of unmarried males = (5 / 8) * 100 = 62.5%, which matches the calculated result. Why Other Options Are Wrong: 125% is impossible as a percentage of a group and clearly incorrect. 84.32% and 46.87% are random looking decimals that do not follow from the ratio calculations. 37.5% is the complement of 62.5% but would represent married males, not unmarried males, under the given data. Common Pitfalls: Students sometimes confuse percentage of total population with percentage of male population. Another mistake is to treat 5/9 and 4/9 as literal numbers instead of proportional values, or to ignore the assumption that each married female pairs with one male. Carefully defining a convenient total population like 9 or a multiple helps keep the arithmetic and logic straightforward. Final Answer: The percentage of unmarried males among the total male population is 62.5%.

Question 7

The current birth rate in a region is 32 per thousand people and the corresponding death rate is 11 per thousand people. What is the net growth rate of the population expressed as a percentage increase per year?

Accepted Answer

Introduction / Context: This question focuses on interpreting crude birth and death rates, commonly given as numbers per thousand population. The net population growth rate is determined by the difference between birth and death rates. Converting that net value into a percentage of the total population is a standard task in population studies and basic demographic mathematics. Given Data / Assumptions: Birth rate = 32 per 1000 population. Death rate = 11 per 1000 population. Net growth rate is taken as births minus deaths per 1000 people. We need the net growth rate as a percentage. Concept / Approach: The net increase per 1000 people is given by: net increase per 1000 = birth rate − death rate. Once we find this net figure, we convert it to a percentage by interpreting it as so many per 1000, and then expressing that as an equivalent per 100 (percent). Since percent means per hundred, dividing the per thousand figure by 10 gives the net growth in percent. Step-by-Step Solution: Step 1: Net increase per 1000 people = birth rate − death rate.Net increase = 32 − 11 = 21 per 1000.Step 2: Convert 21 per 1000 to a percentage (per 100).21 per 1000 = 21 / 1000.Multiply by 100 to get percentage: (21 / 1000) * 100 = 2.1%.Step 3: Therefore the net growth rate is 2.1% per year. Verification / Alternative check: Think of a population of 1000 people. In one year, there are 32 births and 11 deaths, so the population increases by 21, ending at 1021. The growth factor is 1021 / 1000 = 1.021. As a percentage, the growth is (1.021 − 1) * 100 = 2.1%. This is consistent with the earlier direct calculation. Why Other Options Are Wrong: 1.2%, 1.3%, and 2.5% are not equal to 21 / 1000 expressed as a percentage. 3.1% would correspond to a net increase of 31 per 1000, which does not match the given rates. Common Pitfalls: Some students mistakenly add birth and death rates instead of subtracting them, or attempt to average them. Others confuse per thousand with percentage and forget to divide by 10 to move from per 1000 to per 100. Always remember that net growth is births minus deaths, and that converting from per 1000 to percent requires multiplying by 100 and dividing by 1000. Final Answer: The net population growth rate is 2.1% per year.

Question 8

A man plays a gambling game in which, in each round he wins Rs. 100 but must give away 50% of his total amount at the end of that round. He plays three rounds and wins all three games. After these rounds he has lost exactly half of his initial amoun…

Accepted Answer

Introduction / Context: This is a multi step percentage and algebra puzzle that tests careful reading and systematic calculation. In each round of the gambling game, the player first wins a fixed sum of money and then must give away half of his total amount. After three such rounds, his final amount is exactly half of his original amount. From this information, you must work backwards to recover the initial amount of money. Given Data / Assumptions: The man starts with some initial amount of money, say X rupees. In each round he wins Rs. 100. At the end of every round he must give away 50% of his total amount at that moment. He plays 3 rounds and wins all 3. After the three rounds he has lost half of his initial amount, so his final amount equals X / 2. Concept / Approach: We treat this as a stepwise process. Let the amount after round 1 be A1, after round 2 be A2, and after round 3 be A3. For each round, the sequence is: add Rs. 100 to the current amount, then halve it. So A1 = (X + 100) / 2, A2 = (A1 + 100) / 2, and A3 = (A2 + 100) / 2. We then set A3 equal to X / 2 and solve for X using algebra. This gives a linear equation in X. Step-by-Step Solution: Step 1: Let initial amount = X rupees.Step 2: After round 1: he wins 100, so amount becomes X + 100. He then gives away half, so A1 = (X + 100) / 2.Step 3: After round 2: starting from A1, he wins 100, new amount = A1 + 100, then gives half, so A2 = (A1 + 100) / 2.Step 4: After round 3: starting from A2, he wins 100, new amount = A2 + 100, then gives half, so A3 = (A2 + 100) / 2.Step 5: We are told A3 equals half of the initial amount, so A3 = X / 2.Step 6: Substitute A1 and A2 step by step. First A1 = (X + 100) / 2.A2 = (A1 + 100) / 2 = ((X + 100) / 2 + 100) / 2.A3 = (A2 + 100) / 2.After simplifying this expression, we obtain A3 = X / 8 + 175 / 2.Step 7: Set X / 8 + 175 / 2 equal to X / 2.So X / 8 + 175 / 2 = X / 2.Step 8: Multiply through by 8 to clear denominators: X + 700 = 4X.Step 9: Rearrange: 4X − X = 700, so 3X = 700 and X = 700 / 3. Verification / Alternative check: Calculate the amounts numerically starting from X = 700 / 3. Round 1: X + 100 = 700 / 3 + 100 = 1000 / 3. After giving half: A1 = 1000 / 3 / 2 = 500 / 3. Round 2: A1 + 100 = 500 / 3 + 100 = 800 / 3. After giving half: A2 = 800 / 3 / 2 = 400 / 3. Round 3: A2 + 100 = 400 / 3 + 100 = 700 / 3. After giving half: A3 = 700 / 3 / 2 = 350 / 3. Since initial amount X = 700 / 3, half of X is 350 / 3, which equals A3. This confirms the solution. Why Other Options Are Wrong: 500/3, 300, 400, and 600 do not satisfy the relation that the final amount after three rounds equals half of the starting amount when you simulate the process step by step. Common Pitfalls: Common errors include halving before adding 100 instead of after, or applying 50% to the wrong intermediate amount. Some candidates also simplify too early or incorrectly handle fractions, leading to algebraic mistakes. The safest method is to write expressions carefully for each round, check the recursion, and then solve the final equation systematically. Final Answer: The initial amount of money was 700/3 rupees.

Question 9

In a college, the number of boys is 75% of the number of girls, and the difference between the numbers of girls and boys is 35. On a particular day, 20% of the boys are absent. How many boys are present in the college on that day?

Accepted Answer

Introduction / Context: This question combines percentage and difference relationships between two groups, boys and girls, with an absence scenario. The goal is to determine the actual number of boys present on a particular day using given percentage based ratios and a fixed numerical difference. This structure is very typical in aptitude problems involving school or college populations. Given Data / Assumptions: Number of boys is 75% of the number of girls. Difference between the numbers of girls and boys is 35. On a particular day, 20% of the boys are absent. We need to find the number of boys present on that day. Concept / Approach: First, translate the 75% relationship into an equation between boys (B) and girls (G). Then use the given difference G − B = 35 to solve for B and G. After finding the total number of boys, compute 20% absent and subtract that from the total to obtain the number of boys present. This uses both algebra and percentage calculations in a straightforward way. Step-by-Step Solution: Step 1: Let number of girls be G and number of boys be B.Step 2: Boys are 75% of girls, so B = 75% of G = (75 / 100) * G = (3 / 4) * G.Step 3: The difference between girls and boys is 35: G − B = 35.Step 4: Substitute B = (3 / 4) * G into this equation: G − (3 / 4) * G = 35.Step 5: Simplify: (1 − 3 / 4) * G = (1 / 4) * G = 35.Step 6: Hence G = 35 * 4 = 140.Step 7: Boys B = (3 / 4) * 140 = 105.Step 8: On the particular day, 20% of the boys are absent.Absent boys = 20% of 105 = (20 / 100) * 105 = 21.Step 9: Boys present = total boys − absent boys = 105 − 21 = 84. Verification / Alternative check: Check the values: girls = 140, boys = 105. Boys are 105 / 140 = 0.75 = 75% of girls and the difference is 140 − 105 = 35, exactly as given. On the given day, 20% of 105 equals 21 absent, leaving 84 present. Everything is consistent with the problem statement. Why Other Options Are Wrong: 72, 93, 81, and 70 do not result from the correct combination of the ratio, the difference of 35, and the 20% absence calculation. They either correspond to wrong intermediate values or incorrect application of the percentage step. Common Pitfalls: Some students may reverse the 75% relationship and mistakenly set G = 75% of B. Others lose track of whether the 20% is taken of boys or total students. Another frequent mistake is to use the difference 35 directly as 25% of some value without properly setting up equations. Always define variables clearly and translate every relationship systematically into algebraic form before solving. Final Answer: The number of boys present in the college on that day is 84.

Question 10

A seller charges 28% Goods and Services Tax (GST) on an article. If the customer pays a total of Rs. 4544 including GST, what is the cost price (price before GST) of the article?

Accepted Answer

Introduction / Context: This problem involves reversing a percentage increase, specifically GST added on a price. The total amount paid by the customer already includes the tax. To find the original cost of the article, you must consider the total bill as a certain percentage of the base price and then work backwards using simple algebra. Given Data / Assumptions: GST rate applied on the article = 28%. Total amount paid by the customer (price including GST) = Rs. 4544. GST is calculated on the cost price of the article. We need to find the price of the article before GST was added. Concept / Approach: If the cost price is C, then GST at 28% means tax amount = 28% of C = (28 / 100) * C. Therefore the total bill paid by the customer is C + 0.28C = 1.28C. We know that this total is Rs. 4544. So we can write 1.28C = 4544 and solve for C by dividing the total by 1.28. Step-by-Step Solution: Step 1: Let cost price of the article (before GST) be C rupees.Step 2: GST at 28% on C is (28 / 100) * C = 0.28C.Step 3: Total price including GST = C + 0.28C = 1.28C.Step 4: Given that 1.28C = 4544.Step 5: Solve for C: C = 4544 / 1.28.Step 6: Compute 4544 / 1.28 = 3550.Step 7: Therefore the cost price of the article is Rs. 3550. Verification / Alternative check: Check by applying GST forward. 28% of 3550 = (28 / 100) * 3550 = 0.28 * 3550 = 994. Then cost price plus GST = 3550 + 994 = 4544, which matches the amount the customer paid. Hence the calculated cost price is correct. Why Other Options Are Wrong: Rs. 2650, Rs. 2450, and Rs. 3200 are too low; adding 28% GST to those values will result in a total far below Rs. 4544. Rs. 3840 is too high; after adding 28% GST, the total would exceed Rs. 4544. Common Pitfalls: Many candidates simply subtract 28% of 4544 from 4544, which is incorrect because GST is 28% of the cost price, not 28% of the final amount. Another frequent error is to multiply 4544 by 0.28 directly to get the GST rather than first recovering the base. Remember that if total = base * (1 + rate), then base = total / (1 + rate). This pattern appears in many tax and discount problems. Final Answer: The cost price of the article before GST was Rs. 3550.

Question 11

In an election, a candidate received 35% of the votes polled and lost to his rival by 2250 votes. Assuming there were only two candidates, how many total votes were cast in the election?

Accepted Answer

Introduction / Context: This election problem combines percentage vote shares with an absolute margin of defeat to determine the total number of votes polled. Such questions are common in quantitative aptitude to test proportional reasoning and understanding of complementary percentages that sum to 100 when there are only two candidates. Given Data / Assumptions: There are two candidates in the election. The losing candidate receives 35% of the total votes. The winning candidate receives the remaining 65% of the votes. The margin of defeat is 2250 votes. We must find the total number of votes cast. Concept / Approach: If total votes are V, the losing candidate has 0.35V votes, and the winner has 0.65V votes. The difference between their votes is 0.65V − 0.35V = 0.30V. This difference is given as 2250 votes. Thus we set 0.30V equal to 2250 and solve for V. This is a direct algebraic application of the definition of percentage and difference. Step-by-Step Solution: Step 1: Let total votes be V.Step 2: Votes received by the losing candidate = 35% of V = 0.35V.Step 3: Votes received by the winning candidate = 65% of V = 0.65V.Step 4: Margin of victory = votes of winner − votes of loser = 0.65V − 0.35V = 0.30V.Step 5: We are told this margin equals 2250 votes, so 0.30V = 2250.Step 6: Solve for V: V = 2250 / 0.30.Step 7: 0.30 is 3 / 10, so V = 2250 * 10 / 3 = 22500 / 3 = 7500. Verification / Alternative check: Check with the found total: 35% of 7500 = 0.35 * 7500 = 2625 votes. 65% of 7500 = 0.65 * 7500 = 4875 votes. The difference 4875 − 2625 = 2250 votes, exactly as stated. Thus, the result is consistent and correct. Why Other Options Are Wrong: If total votes were 6200, then 30% would be 1860, not 2250. For 5600, 30% is 1680, again not equal to the given margin. For 4700, 30% is 1410 votes, which is too small. 9000 votes would give a margin of 2700 votes, which overshoots the given value. Common Pitfalls: Some students incorrectly compute the margin as 35% of votes instead of the difference between 65% and 35%. Others mis-handle the proportion, taking 2250 as 35% instead of 30%. Always remember that when only two candidates are present, their vote percentages add up to 100%, and the margin corresponds to the difference between these percentages applied to the total votes. Final Answer: The total number of votes cast in the election was 7500.

Question 12

A restaurant sells cakes at an original price of Rs. 12 each and earlier sold 250 cakes per day. It introduces a promotion offering a 20% discount on the price of each cake. After the promotion, daily sales of cakes increase by 18% in quantity. Comp…

Accepted Answer

Introduction / Context: This problem tests understanding of the combined impact of a price discount and a demand increase on total revenue. It mimics real life business scenarios, where lowering the price can boost sales volume, and you must determine whether total revenue rises or falls. The key is to treat revenue as price multiplied by quantity and compare the before and after cases. Given Data / Assumptions: Original price per cake = Rs. 12. Original number of cakes sold per day = 250. New discount offered = 20% off the original price. After the discount, number of cakes sold per day increases by 18%. We assume these are the only changes; costs and other factors stay the same. Concept / Approach: Compute original revenue per day as original price times original quantity. Then compute the new price after a 20% discount and the new quantity after an 18% increase. Multiply these to obtain the new daily revenue. The difference between new revenue and original revenue tells us how much more or less the restaurant makes each day. Step-by-Step Solution: Step 1: Original price per cake = Rs. 12.Step 2: Original number of cakes sold per day = 250.Step 3: Original revenue = 12 * 250 = Rs. 3000 per day.Step 4: New price after 20% discount = 12 * (1 − 20 / 100) = 12 * 0.80 = Rs. 9.6 per cake.Step 5: New quantity after 18% increase = 250 * (1 + 18 / 100) = 250 * 1.18 = 295 cakes per day.Step 6: New revenue = 9.6 * 295.Compute: 9.6 * 295 = 2832.Step 7: Change in daily revenue = new revenue − original revenue = 2832 − 3000 = −168.Step 8: Negative sign indicates a loss of Rs. 168 per day. Verification / Alternative check: Express new revenue as a factor of old revenue. Price factor = 0.80 due to 20% discount. Quantity factor = 1.18 due to 18% increase in sales. Combined revenue factor = 0.80 * 1.18 = 0.944. So new revenue is 94.4% of old revenue. 94.4% of 3000 = 0.944 * 3000 = 2832. The loss is 3000 − 2832 = 168, which matches the previous method. Why Other Options Are Wrong: Rs. 185 less and Rs. 150 less do not arise from the actual product of price and quantity changes. Rs. 202 more and Rs. 175 more would imply that revenue increased, which contradicts both the factor calculation and the direct computation. Common Pitfalls: Common errors include subtracting 20% and adding 18% directly to the revenue, instead of adjusting both price and quantity first and then multiplying. Another mistake is to miscalculate the updated quantity or to forget that the 18% increase applies to the original 250 cakes. Always treat revenue as the product of price and quantity and apply separate percentage changes correctly to each factor. Final Answer: After the promotion, the restaurant makes Rs. 168 less per day from cake sales.

Question 13

In a factory there are three types of machines M1, M2 and M3 which produce 25%, 35% and 40% of the total output respectively. Machines M1, M2 and M3 produce 2%, 4% and 5% defective products respectively. What percentage of the total products manufac…

Accepted Answer

Introduction / Context: This question is about weighted probabilities and percentages. Each machine contributes a different share of the total production and also has its own defective rate. To find the overall percentage of non defective items, you must weight each machine defect rate by its share in the total production and subtract the resulting overall defect rate from 100%. Given Data / Assumptions: Machine M1 produces 25% of the total products and 2% of these are defective. Machine M2 produces 35% of the total products and 4% of these are defective. Machine M3 produces 40% of the total products and 5% of these are defective. We assume that all products come from these three machines only. Concept / Approach: The overall defective percentage is the sum of the defective contributions from each machine. For each machine, we multiply its share of total production by its defect rate. The overall non defective percentage is then 100% minus the overall defective percentage. This is a classic application of the law of total probability in percentage form. Step-by-Step Solution: Step 1: Consider total production as 100 units for easy calculation.Step 2: Units produced by M1 = 25% of 100 = 25 units.Step 3: Units produced by M2 = 35% of 100 = 35 units.Step 4: Units produced by M3 = 40% of 100 = 40 units.Step 5: Defective units from M1 = 2% of 25 = (2 / 100) * 25 = 0.5 units.Step 6: Defective units from M2 = 4% of 35 = (4 / 100) * 35 = 1.4 units.Step 7: Defective units from M3 = 5% of 40 = (5 / 100) * 40 = 2 units.Step 8: Total defective units = 0.5 + 1.4 + 2 = 3.9 units out of 100.Step 9: Overall defective percentage = 3.9%.Step 10: Overall non defective percentage = 100% − 3.9% = 96.1%. Verification / Alternative check: Instead of working with units, work directly with percentages. Contribution to defect rate from M1 = 0.25 * 2% = 0.5%. From M2 = 0.35 * 4% = 1.4%. From M3 = 0.40 * 5% = 2%. Sum = 0.5% + 1.4% + 2% = 3.9%. Non defective percentage = 100% − 3.9% = 96.1%. Both methods are identical and confirm the answer. Why Other Options Are Wrong: 89% and 86.1% are much too low and would correspond to a much higher overall defect rate than the data support. 97.1% is slightly higher than the correct 96.1% and does not match the summed contributions of the three machines. 92.9% is another distractor value and does not arise from any correct weighting calculation. Common Pitfalls: Some students incorrectly average the defect rates 2%, 4% and 5% without weighting by production share, which ignores the fact that M3 produces more items. Others mistakenly add the production percentages before multiplying by defect percentages. Always remember to multiply each machine share by its own defect rate and then add these contributions to find the overall defect rate. Final Answer: The percentage of non defective products manufactured by the factory is 96.1%.

Question 14

One-third of the boys and one-half of the girls in a college participate in a sports event. If 300 students participate in total and 100 of them are boys, what is the total number of students in the college?

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Introduction / Context: This aptitude question tests understanding of percentages, fractions, and basic algebra involving two groups, boys and girls, in a college. The goal is to convert the verbal conditions into equations and then determine the total strength of the college based on how many students participate in a sports event. This pattern of question is very common in competitive exams because it checks comfort with percentages and translation of words into numbers. Given Data / Assumptions: One-third of the boys participate in the event. One-half of the girls participate in the event. Total participating students are 300. Out of these 300 participants, 100 are boys. Total number of students equals total boys plus total girls. Concept / Approach: The idea is to represent the number of boys and girls using variables, and then use the percentage information to build equations. Since we know exactly how many participating boys there are, that gives us one direct equation. The total number of participants gives a second equation. Solving these gives the total number of boys and girls separately, and adding them gives the total student population. This is a straightforward system of linear equations in two variables. Step-by-Step Solution: Step 1: Let the total number of boys be B and the total number of girls be G.Step 2: One-third of the boys participate, and the number of participating boys is given as 100. So (1/3) * B = 100, which implies B = 300.Step 3: Total participants are 300. Out of them, 100 are boys, so participating girls are 300 - 100 = 200.Step 4: One-half of the girls participate, so (1/2) * G = 200, which implies G = 400.Step 5: The total number of students in the college is B + G = 300 + 400 = 700. Verification / Alternative check: Check the fractions with the found values. One-third of 300 boys is 100, which matches the given participating boys. One-half of 400 girls is 200, which together with 100 boys gives 300 total participants. All given conditions are satisfied, so the answer is consistent and verified. Why Other Options Are Wrong: For 500, there is no way to split into boys and girls while keeping the given participation numbers of 100 boys and 200 girls. For 300, that would mean everyone is participating, contradicting the fraction conditions. For 600, the participation fractions would not match the given participant counts. For 650, similar algebra would fail to produce one-third equal to 100 and one-half equal to 200. Only 700 allows both equations to hold simultaneously. Common Pitfalls: Many students confuse the total number of participants with the total number of students or treat the given percentages as percentages of 300 rather than as fractions of the separate boy and girl populations. Another common mistake is to misread that 100 are boys and assume 200 are girls without then using the one-half relationship correctly. Careful reading and systematic use of variables help to avoid these mistakes. Final Answer: The total number of students in the college is 700, so the correct option is 700.

Question 15

Twenty five percent of twenty five percent of a quantity is equal to which decimal value?

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Introduction / Context: This is a simple percentage and decimal conversion question. It asks you to compute a percentage of another percentage and then express the final result in decimal form. Such questions test basic understanding of how percentages convert to decimals and how to multiply them correctly without confusion. Given Data / Assumptions: We are given 25 percent of 25 percent of some quantity. No actual base quantity is specified, so we can use a convenient assumed value if needed. The final answer must be expressed as a decimal number. Concept / Approach: Percent means per hundred. So 25 percent is 25/100 or 0.25 in decimal form. To find 25 percent of 25 percent, we multiply 0.25 by 0.25. It does not matter what the original quantity is, because we are only asked for the fraction of that quantity in decimal form. When two percentages are applied successively to the same base, you simply multiply their decimal representations. Step-by-Step Solution: Step 1: Convert 25 percent to decimal: 25 percent = 25/100 = 0.25.Step 2: Compute 25 percent of 25 percent as 0.25 * 0.25.Step 3: Multiply 0.25 by 0.25 to get 0.0625.Step 4: Therefore, 25 percent of 25 percent of any quantity is equal to 0.0625 times that quantity. Verification / Alternative check: As a check, assume the base quantity is 1. Then 25 percent of 1 is 0.25. Now take 25 percent of 0.25, which is 0.25 * 0.25 = 0.0625. This matches our calculation. If we took a different base, say 100, then 25 percent of 100 is 25, and 25 percent of 25 is 6.25. As a fraction of 100, 6.25 is still 0.0625, so the value is consistent. Why Other Options Are Wrong: The value 0.0210 corresponds to 2.1 percent, which is smaller than 6.25 percent and does not match the multiplication of 0.25 by 0.25. The value 0.03145 is an arbitrary decimal with no relation to the simple product of 0.25 and 0.25. The value 0.3210 would be 32.1 percent, much larger than expected. The value 0.2500 would represent just 25 percent, not 25 percent of 25 percent. Only 0.0625 is correct. Common Pitfalls: A common mistake is to add percentages instead of multiplying them, for example taking 25 percent of 25 percent as 50 percent or 0.5, which is incorrect. Another error is to misplace decimal points when converting percentages to decimals, such as writing 25 percent as 0.025. Remember that to convert a percentage to a decimal, you divide by 100, and to apply one percentage after another, you multiply their decimal values. Final Answer: The decimal value corresponding to 25 percent of 25 percent is 0.0625, so the correct option is 0.0625.

Question 16

Lagaan, a land revenue tax, is levied on 60 percent of the cultivated land of a village. The total lagaan collected is Rs. 3,84,000 and farmer Sukhiya pays Rs. 480. What percentage of the taxable land area of the village belongs to Sukhiya?

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Introduction / Context: This question deals with percentage share and proportional reasoning in the context of land revenue, called lagaan. The tax is levied uniformly on taxable land, so the lagaan paid by a single farmer is directly proportional to the taxable land area owned by that farmer. We have to convert this relationship into a percentage of the total taxable land. Given Data / Assumptions: Lagaan is levied on 60 percent of the cultivated land in the village, called taxable land. Total lagaan collected from all taxable land is Rs. 3,84,000. Farmer Sukhiya pays lagaan of Rs. 480. Lagaan per unit area of taxable land is uniform for all farmers. We need the percentage of Sukhiya land as a share of the total taxable land. Concept / Approach: Since lagaan is directly proportional to taxable land area and the rate is the same for everyone, the ratio of Sukhiya tax to total lagaan is equal to the ratio of his taxable land to the total taxable land. Therefore percentage share of taxable land can be found simply as (Sukhiya lagaan divided by total lagaan) multiplied by 100. The 60 percent information tells us which part of total cultivated land is taxed, but for this calculation we only care about the taxed portion because both numerator and denominator refer to taxable land only. Step-by-Step Solution: Step 1: Let total taxable land area be T units and Sukhiya taxable land be S units.Step 2: Since lagaan is uniform, lagaan is proportional to area. Therefore S / T = Sukhiya lagaan / total lagaan.Step 3: Substitute values: S / T = 480 / 384000.Step 4: Compute the fraction 480 / 384000. This simplifies to 1 / 800.Step 5: Convert this fraction into percentage: (1 / 800) * 100 = 0.125 percent. Verification / Alternative check: Check with mental calculation by reducing stepwise. Divide numerator and denominator by 48: 480 / 48 = 10, 384000 / 48 = 8000. So the fraction becomes 10 / 8000, which reduces to 1 / 800. Now think of 1 percent as 1 / 100. Then 1 / 800 is eight times smaller than 1 / 100, so it is 0.125 percent, since 1 / 8 equals 0.125. This confirms our result without a calculator. Why Other Options Are Wrong: The value 0.15 percent is slightly larger than the correct share and does not match the precise ratio. The value 15 percent is far too large, suggesting that Sukhiya pays a huge portion of the village tax, which contradicts the small payment of Rs. 480 compared with Rs. 3,84,000. The value 1.25 percent is ten times the correct fraction. The value 0.25 percent is exactly double the correct share. Only 0.125 percent matches the computed proportion S / T. Common Pitfalls: A common mistake is to confuse 0.125 with 12.5 percent or 1.25 percent due to misplaced decimal points. Another issue is to mix up cultivated land and taxable land. In this question, both the total lagaan and Sukhiya lagaan are calculated only on taxable land, so the 60 percent of cultivated land detail does not need to enter the ratio explicitly. Students should focus on the direct proportion between tax paid and taxable area owned. Final Answer: The percentage of total taxable land belonging to Sukhiya is 0.125%, so the correct option is 0.125%.

Question 17

The tax on an article decreases by 10 percent and its consumption increases by 10 percent. What is the net percentage change in the revenue collected on this article?

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Introduction / Context: This question tests the concept of percentage change in a product of two quantities. Revenue is the product of tax per unit and number of units consumed. When one factor decreases by a certain percentage while the other increases, we need to find the overall effect on the product. This is a classic exam pattern that checks comfort with successive percentage change. Given Data / Assumptions: Tax per unit decreases by 10 percent. Consumption (units sold) increases by 10 percent. Revenue = tax per unit multiplied by number of units. We assume a uniform initial tax and fixed base consumption for comparison. Concept / Approach: If a value is reduced by 10 percent, it becomes 90 percent of the original, which is a factor of 0.9. If another value is increased by 10 percent, it becomes 110 percent of the original, which is a factor of 1.1. When two changes affect a product, the new product is the product of the new factors. Therefore, the net change in revenue can be found by multiplying 0.9 and 1.1 and comparing the result to 1, which represents the original revenue. Step-by-Step Solution: Step 1: Let the original tax per unit be T and the original consumption be Q units. Then original revenue is R = T * Q.Step 2: Tax decreases by 10 percent, so the new tax per unit is 0.9T.Step 3: Consumption increases by 10 percent, so the new quantity is 1.1Q.Step 4: New revenue R_new = 0.9T * 1.1Q = 0.99TQ.Step 5: Compare with original revenue R = TQ. The ratio R_new / R = 0.99, which means the new revenue is 99 percent of the original.Step 6: If revenue is 99 percent of the original, the decrease is 1 percent. Verification / Alternative check: Take a simple numerical example. Assume the original tax is Rs. 10 per unit and 100 units are sold, giving original revenue of Rs. 1000. After the change, tax becomes 10 * 0.9 = Rs. 9 and consumption becomes 100 * 1.1 = 110 units. The new revenue is 9 * 110 = Rs. 990. This is Rs. 10 less than 1000, which is a reduction of 1 percent. This numerical check confirms the algebraic reasoning. Why Other Options Are Wrong: A 1 percent increase would require the net factor to be 1.01, not 0.99. A 10 percent decrease would correspond to a net factor of 0.9, which we do not have. No change would require the product of the factors to be exactly 1. The 2 percent increase option corresponds to a factor of 1.02, which again does not match 0.99. Only a 1 percent decrease fits the computed net effect. Common Pitfalls: Many learners add the percentage changes directly and claim 10 percent minus 10 percent equals zero net change. This is incorrect because the changes apply to different factors and the overall effect is multiplicative, not additive. Another error is to ignore the direction of change, mixing increase and decrease incorrectly. Always convert each percentage change into a multiplier and then multiply to find the combined effect on a product. Final Answer: The revenue decreases slightly and becomes 99 percent of the original, so there is a 1% decrease in revenue. Thus the correct option is 1% decrease.

Question 18

Five percent of a number is 25 percent more than another number. The difference between the two numbers is 96. What are the two numbers?

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Introduction / Context: This problem combines percentages with linear equations in two unknown numbers. One number is related to the other through a percentage condition, and the difference between them is given. The question is a typical algebraic word problem found in competitive exams, checking whether you can translate language into equations and solve them systematically. Given Data / Assumptions: Let the first number be x and the second number be y. Five percent of x is 25 percent more than y. The difference between the two numbers x and y is 96. We assume both numbers are positive real numbers and expect integer answers based on the options. Concept / Approach: We need to form two equations. The first equation comes from the statement that 5 percent of x is 25 percent more than y. The phrase 25 percent more than y means y plus 25 percent of y, which is 1.25y. The second equation is simply x minus y equals 96. Solving this pair of linear equations yields values for x and y. Then we can match the ordered pair with the given options. Step-by-Step Solution: Step 1: Translate the percentage condition. Five percent of x is 0.05x. It is given that 0.05x = 1.25y.Step 2: From 0.05x = 1.25y, divide both sides by 0.05 to express x in terms of y. We get x = (1.25 / 0.05) * y = 25y.Step 3: Use the difference condition x - y = 96.Step 4: Substitute x = 25y into x - y = 96 to get 25y - y = 96.Step 5: Simplify to 24y = 96, so y = 96 / 24 = 4.Step 6: Substitute back to find x: x = 25y = 25 * 4 = 100. Verification / Alternative check: Check the percentage condition with x = 100 and y = 4. Five percent of 100 is 5. Now find 25 percent more than y: 25 percent of 4 is 1, so 4 plus 1 equals 5. The condition 0.05x = 1.25y is satisfied. The difference x - y equals 100 - 4 = 96, which matches the given difference. Therefore the pair (100, 4) is fully consistent with both conditions. Why Other Options Are Wrong: For 102 and 6, the difference is 96 but 5 percent of 102 is 5.1, which is not 25 percent more than 6. For 99 and 3, the difference is 96 but 5 percent of 99 is 4.95, while 25 percent more than 3 is 3.75. For 104 and 8, the difference is 96, but 5 percent of 104 is 5.2 and 25 percent more than 8 is 10. For 120 and 24, 5 percent of 120 is 6, but 1.25 times 24 is 30. Only 100 and 4 satisfy both conditions exactly. Common Pitfalls: Some students misinterpret 25 percent more than y as simply 0.25y instead of y plus 0.25y. Others might incorrectly treat percentages as whole numbers or forget to convert them to decimals. Another common error is forming incorrect equations, such as 0.05x = 0.25y, which would not reflect the phrase 25 percent more than y. Careful attention to wording and algebraic manipulation prevents these mistakes. Final Answer: The two numbers are 100 and 4, so the correct option is 100 and 4.

Question 19

One hundred percent of which number is equal to 20?

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Introduction / Context: This is a very basic percentage question that checks whether you understand that 100 percent of a quantity simply means the entire quantity. It is useful as a warm-up and reinforces the meaning of percentage as a fraction of 100. Given Data / Assumptions: We are told that 100 percent of some number equals 20. We must find that original number. All numbers are real and we expect a simple answer from the options given. Concept / Approach: Percent literally means per hundred. So 100 percent is 100 divided by 100, which equals 1. Multiplying any number by 1 returns the number itself. Therefore, when a question says that 100 percent of some number is 20, it means the number itself is 20. We can also express this with a simple equation using basic multiplication. Step-by-Step Solution: Step 1: Let the unknown number be N.Step 2: Translate the statement 100 percent of N is 20 into an equation. Since 100 percent equals 100 / 100 = 1, we have 1 * N = 20.Step 3: This simplifies directly to N = 20.Step 4: Therefore the original number is 20. Verification / Alternative check: Take N = 20 and compute 100 percent of N in the usual way. One hundred percent of 20 is (100 / 100) * 20 = 1 * 20 = 20. This matches the given value. No other number can satisfy the equation 1 * N = 20, so the answer is unique and verified. Why Other Options Are Wrong: If the number were 100, then 100 percent of it would be 100, not 20. If the number were 500, then 100 percent of it would be 500. If the number were 0, 100 percent of it would be 0. For 10, 100 percent of 10 would be 10. None of these equal 20. Only when the number itself is 20 do we get 100 percent of the number equal to 20. Common Pitfalls: Sometimes students confuse 100 percent with 100 or treat percent as a separate operation that changes the value in an unexpected way. Remember that 100 percent is exactly equal to 1 as a multiplier, so it does not change the value at all. Another mistake is to overthink the problem and attempt unnecessary calculations, when the direct interpretation is sufficient. Final Answer: The original number whose 100 percent is 20 is 20, so the correct option is 20.

Question 20

One-fourth of one-seventh of a plot of land is sold for Rs. 30,000. What is the value of four-fifteenths of the same land?

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Introduction / Context: This question tests the ability to work with fractions of a whole and proportional values. We are given the sale price of a certain fractional part of a plot of land and asked to find the value of another fractional part of the same land. Since the land has uniform value per unit area, the price is directly proportional to the fraction of land. Given Data / Assumptions: One-fourth of one-seventh of the plot is sold for Rs. 30,000. The land is assumed to have uniform value per unit area. We must find the value of four-fifteenths (4/15) of the same land. No change in price per unit area is implied, so the rate is constant. Concept / Approach: If 1/4 of 1/7 of the land is worth Rs. 30,000, we can compute the total value of the entire plot by dividing by that fractional share. Once we know the total value of the full land, we can multiply by 4/15 to get the value of four-fifteenths. The key is to handle fractions carefully, noting that 1/4 of 1/7 equals 1/28 of the full land. Step-by-Step Solution: Step 1: The fraction 1/4 of 1/7 is (1/4) * (1/7) = 1/28.Step 2: One twenty eighth of the plot is sold for Rs. 30,000.Step 3: Let the total value of the land be V. Then (1/28) * V = 30,000.Step 4: Solve for V: V = 30,000 * 28 = 8,40,000.Step 5: We need the value of 4/15 of the land, which is (4/15) * V = (4/15) * 8,40,000.Step 6: Compute (4/15) * 8,40,000. First find 8,40,000 / 15 = 56,000, then multiply by 4 to get 2,24,000. Verification / Alternative check: We can check the consistency of the values. If the whole land is worth Rs. 8,40,000, then 1/28 of it is 8,40,000 / 28. Since 28 * 30,000 equals 8,40,000, the small portion worth Rs. 30,000 is indeed 1/28. For the target fraction, 4/15 of 8,40,000 should equal 2,24,000, and multiplying 56,000 by 4 confirms this. All steps align, so the computation is correct. Why Other Options Are Wrong: The value Rs. 1,92,000 is smaller than 2,24,000 and would correspond to a smaller fraction such as 4/17.5 of the land, not 4/15. The value Rs. 1,26,000 is much smaller and does not match any simple fraction of 8,40,000 related to the given conditions. The value Rs. 3,42,000 is larger and would correspond to approximately 4/9.8 of the land. The value Rs. 2,80,000 is also inconsistent with 4/15 of the total. Only Rs. 2,24,000 matches the exact computed value of 4/15 of the total land value. Common Pitfalls: A frequent mistake is to misinterpret 1/4 of 1/7 as 1/11 or 1/4 + 1/7 instead of the product 1/28. Another error occurs when students try to go directly from 30,000 to 4/15 of the land without first finding the total value. Also, some may perform fraction operations or division incorrectly, especially when dealing with large numbers. Breaking the calculation into smaller steps, such as simplifying 8,40,000 / 15 before multiplying by 4, helps to avoid arithmetic errors. Final Answer: The value of four-fifteenths of the land is Rs.2,24,000, so the correct option is Rs.2,24,000.

Percentage Questions