Question 1

Suresh starts working as an analyst with an annual salary of Rs. 1,60,000. He receives a 15% pay rise every year. After how many complete years will his annual salary become Rs. 2,79,841?

Accepted Answer

Introduction / Context: This is a compound percentage growth problem involving annual salary increments. Suresh receives a fixed percentage raise each year, and we are asked to determine how many years it takes for his salary to reach a specified amount. This type of question mirrors real life salary growth scenarios and tests understanding of repeated percentage increases compounded over time. Given Data / Assumptions: Initial annual salary = Rs. 1,60,000. Annual pay rise = 15% of the current salary. Final salary after some years = Rs. 2,79,841. We must find the number of complete years required. Concept / Approach: A salary that increases by a fixed percentage each year follows a compound growth pattern. If the initial salary is S and the growth rate per year is r, then after n years the salary is S * (1 + r)^n. Here, S = 160000 and r = 0.15. We need to find n such that 160000 * (1.15)^n = 279841. Since the options are discrete small numbers of years, it is efficient to compute the salary year by year and compare it with the target value. Step-by-Step Solution: Step 1: Initial salary in year 0 is 160000. Step 2: After 1 year: Salary = 160000 * 1.15 = 184000. Step 3: After 2 years: Salary = 184000 * 1.15 = 211600 (approximately). Step 4: After 3 years: Salary = 211600 * 1.15 ≈ 243340. Step 5: After 4 years: Salary = 243340 * 1.15. Step 6: Compute year 4 salary exactly: 160000 * (1.15)^4. Step 7: 1.15^2 = 1.3225, and 1.15^4 = 1.3225^2 ≈ 1.748. Step 8: 160000 * 1.748 ≈ 279680, and more accurate computation gives 279841. Step 9: Thus after 4 years, salary is Rs. 2,79,841, matching the given final salary. Verification / Alternative check: We can compute step by step more precisely. Year 1: 160000 * 1.15 = 184000. Year 2: 184000 * 1.15 = 211600. Year 3: 211600 * 1.15 = 243340. Year 4: 243340 * 1.15 = 279841 exactly. Since the fourth year value matches the target salary and earlier years are below it, we confirm that 4 years is the required duration. Why Other Options Are Wrong: 3.5 years and 4.5 years are not meaningful in this context because increments are applied yearly and the question asks for complete years. After 3 years, the salary is 243340, which is still below 279841. After 5 years, the salary would exceed 279841, so 5 years is too long. The option "Cannot be determined" is incorrect because the information provided is sufficient to find the exact year count. Only 4 years fits the data. Common Pitfalls: Some learners may mistakenly apply simple interest style calculations, adding 15% of the original salary each year instead of compounding on the updated salary. Others might round too aggressively at intermediate steps, leading to a slightly different final salary and confusion. Using a structured compound interest formula or careful year by year multiplication avoids these errors. Final Answer: Suresh's annual salary becomes Rs. 2,79,841 after 4 yrs of working with 15% yearly increments.

Question 2

In a test, 14% of the students failed in Mathematics and 22% failed in Hindi. If 18% of the students failed in both subjects, what percentage of students passed in both Mathematics and Hindi?

Accepted Answer

Introduction / Context: This problem uses the concept of set intersection and union with percentages, specifically the idea of overlapping groups of students failing in different subjects. It tests understanding of inclusion exclusion principles with percentages and helps develop reasoning about students passing or failing in multiple subjects simultaneously. Given Data / Assumptions: 14% of students failed in Mathematics. 22% of students failed in Hindi. 18% of students failed in both Mathematics and Hindi. We assume percentages are taken out of the same total student population. We must find the percentage of students who passed in both subjects. Concept / Approach: Let the total student population represent 100%. Let F_M be the set of students failing in Mathematics and F_H be the set failing in Hindi. The percentage failing in at least one subject is given by the union F_M ∪ F_H. Using the inclusion exclusion principle, the percentage in the union is P(F_M) + P(F_H) - P(F_M ∩ F_H). Students who pass both subjects are those not in the union, so we subtract this union percentage from 100%. Step-by-Step Solution: Step 1: Let total students represent 100%. Step 2: Percentage failing in Mathematics, P(F_M) = 14%. Step 3: Percentage failing in Hindi, P(F_H) = 22%. Step 4: Percentage failing in both subjects, P(F_M ∩ F_H) = 18%. Step 5: Percentage failing in at least one subject, P(F_M ∪ F_H) = P(F_M) + P(F_H) - P(F_M ∩ F_H). Step 6: Substitute values: P(F_M ∪ F_H) = 14 + 22 - 18 = 18%. Step 7: Therefore, 18% of students fail in at least one of the two subjects. Step 8: Students who pass both subjects = 100% - 18% = 82%. Step 9: Hence, 82% of the students pass in both Mathematics and Hindi. Verification / Alternative check: We can check by assuming a total of 100 students. Then 14 fail Mathematics, 22 fail Hindi, and 18 fail both. The number failing at least one is 14 + 22 - 18 = 18 students. Therefore, 100 - 18 = 82 students pass both subjects. Converting back to percentage, this again gives 82%, matching our earlier result. Why Other Options Are Wrong: 40%, 46%, 54%, and 64% would correspond to much lower pass rates, implying a significantly higher failure rate than the one computed. For example, 40% passing both would mean 60% either failing one or both subjects, which contradicts the computed 18% failing at least one. Only 82% is consistent with the given failure percentages and the inclusion exclusion principle. Common Pitfalls: A common error is to add failure percentages directly (14 + 22 = 36) and then subtract this from 100 to say 64% passed both subjects, which ignores the overlap of 18%. Another mistake is to subtract the intersection twice or to misinterpret the intersection value. Correct application of P(A ∪ B) = P(A) + P(B) - P(A ∩ B) is crucial. Always carefully distinguish between failing at least one subject and failing both subjects. Final Answer: The percentage of students who passed in both subjects is 82%.

Question 3

Ramesh started a software business by investing Rs. 50,000. After six months, Rajesh joined him with a capital of Rs. 75,000. At the end of 3 years, they earned a total profit of Rs. 27,000. Assuming the profit is shared in proportion to capital mul…

Accepted Answer

Introduction / Context: This question is a classic partnership and percentage profit sharing problem. Two partners invest different amounts at different times, and we are asked to divide the total profit according to their effective investment contributions. The effective contribution is determined by multiplying the invested capital by the time period for which it was used. This concept is widely used in partnership questions in aptitude exams. Given Data / Assumptions: Ramesh invested Rs. 50,000 at the start. Rajesh joined after six months with Rs. 75,000. Total duration of the business is 3 years (36 months). Profit at the end of 3 years is Rs. 27,000. Profit is distributed in the ratio of (capital * time) for each partner. Concept / Approach: The effective investment for each partner is capital multiplied by the number of months for which it remains invested. Once we find these products, we can form a ratio. The total profit is then split in this ratio. Specifically, we compute the ratio of Ramesh's effective investment to Rajesh's effective investment and then use this ratio to find Rajesh's share of Rs. 27,000. Step-by-Step Solution: Step 1: Total time for the business is 3 years = 36 months. Step 2: Ramesh invests Rs. 50,000 for all 36 months. Step 3: Rajesh joins after 6 months, so he invests Rs. 75,000 for 30 months. Step 4: Effective investment for Ramesh = 50000 * 36 = 1800000. Step 5: Effective investment for Rajesh = 75000 * 30 = 2250000. Step 6: Ratio of their effective investments is 1800000 : 2250000. Step 7: Simplify the ratio: divide both by 450000 to get 4 : 5. Step 8: Therefore, profit is shared in the ratio 4 : 5 (Ramesh : Rajesh). Step 9: Total profit = 27000, so each ratio part = 27000 / (4 + 5) = 27000 / 9 = 3000. Step 10: Rajesh's share = 5 parts = 5 * 3000 = 15000. Step 11: Hence, Rajesh receives Rs. 15,000 as his share of the profit. Verification / Alternative check: We can compute Ramesh's share as 4 parts = 4 * 3000 = 12000. Then, 12000 + 15000 = 27000, which matches the total profit. Also, the share division 12000 : 15000 simplifies to 4 : 5, matching the ratio of their effective investments. This confirms that the calculation for Rajesh's share is correct. Why Other Options Are Wrong: 10,000 and 12,500 correspond to smaller shares than justified by Rajesh's larger effective investment. 20,000 and 25,000 are too large; they would upset the balance of the 4 : 5 ratio and either exceed the total profit or leave an incorrect amount for Ramesh. Only 15,000 fits the correct investment time ratio and matches the total profit distribution. Common Pitfalls: One common mistake is to ignore the different times for which the investments were made and compare only the raw capital amounts 50000 and 75000. Another is to treat 3 years as 3 months or miscount the months of Rajesh's investment. Students also sometimes invert the ratio or forget to add the ratio parts correctly before dividing the total profit. Careful attention to the time factor and ratio arithmetic is essential. Final Answer: Rajesh's share in the profit is Rs. 15,000.

Question 4

A merchant starts with a certain capital and gains annually at the rate of 30%. At the end of 2 years he is worth Rs. 10,000. What was his original capital at the beginning?

Accepted Answer

Introduction / Context: This question is about compound percentage growth, similar to compound interest, where a merchant's capital grows by 30% every year. The final amount after 2 years is given and we are asked to work backward to find the original capital. This kind of problem is common in quantitative aptitude and financial mathematics and reinforces the concept of reversing compound growth. Given Data / Assumptions: Annual growth rate = 30%. Time period = 2 years. Value after 2 years = Rs. 10,000. Let the original capital be C rupees. Concept / Approach: When capital grows at a rate r per year, the amount after n years is given by C * (1 + r)^n. Here, r = 0.30 and n = 2. So the final amount A is C * (1.30)^2. We know A = 10000, so we set 10000 = C * (1.30)^2 and solve for C. Since (1.30)^2 = 1.69, we have C = 10000 / 1.69. This is a standard reverse compound interest calculation. Step-by-Step Solution: Step 1: Let the original capital be C. Step 2: Annual growth factor = 1 + 30% = 1.30. Step 3: After 2 years, amount A = C * (1.30)^2. Step 4: Compute (1.30)^2 = 1.30 * 1.30 = 1.69. Step 5: We are told that after 2 years, A = 10000, so 10000 = C * 1.69. Step 6: Solve for C: C = 10000 / 1.69. Step 7: Perform the division: 10000 / 1.69 ≈ 5917.16. Step 8: Rounding to the nearest rupee, the original capital is approximately Rs. 5,917. Verification / Alternative check: Verify using C = 5917. If we grow this by 30% for 2 years, the amount should be approximately 10000. After year 1: 5917 * 1.30 ≈ 7692.1. After year 2: 7692.1 * 1.30 ≈ 9999.73, which is effectively 10000 when rounded. This confirms that starting with about 5917 and applying two successive 30% increases leads us to the final value. Why Other Options Are Wrong: Values like 4987, 5148, 6254, and 7000 either produce amounts well below or above 10000 when grown by 30% for 2 years. For example, 7000 * 1.69 = 11830, which is far above 10000. Only 5917 multiplied by 1.69 gives a result close to 10000, so it is the only consistent option with the given data and growth rate. Common Pitfalls: Some learners mistakenly treat the growth as simple interest, adding 30% of the original capital twice instead of compounding. This would lead to using a factor of 1 + 2 * 0.30 = 1.60 instead of 1.69. Others may attempt to subtract 30% twice when working backward, which is not equivalent to dividing by 1.69. Understanding that each year's increase is applied to the new amount, not the original, is crucial to solving such problems correctly. Final Answer: The merchant's original capital was approximately Rs. 5,917.

Question 5

What percentage of a day is equal to 3 hours?

Accepted Answer

Introduction / Context: This question tests a basic understanding of percentages and time. A day has 24 hours, and we are asked to find what percentage 3 hours represents out of a full day. This is a simple ratio to percentage conversion and is commonly used in time management and scheduling problems. Given Data / Assumptions: 1 full day = 24 hours. We are given a time interval of 3 hours. We must express 3 hours as a percentage of 24 hours. Concept / Approach: To find what percentage one quantity is of another, we use the formula: Percentage = (Part / Whole) * 100. Here, the part is 3 hours and the whole is 24 hours. Once we find 3 / 24, we multiply by 100 to get the percentage. It is often useful to simplify the fraction before multiplying to reduce the chance of errors. Step-by-Step Solution: Step 1: Identify the part and the whole. Part = 3 hours, Whole = 24 hours. Step 2: Form the fraction representing the part of the whole: 3 / 24. Step 3: Simplify 3 / 24 by dividing numerator and denominator by 3 to get 1 / 8. Step 4: Convert the fraction to a percentage: (1 / 8) * 100. Step 5: Compute 1 / 8 = 0.125. Step 6: Multiply by 100: 0.125 * 100 = 12.5. Step 7: Therefore, 3 hours is 12.5% of a 24 hour day. Verification / Alternative check: We can also think of a day as divided into eight equal parts of 3 hours each (since 24 / 3 = 8). Each equal part must then correspond to one eighth of the day. As a percentage, one eighth is 12.5%, confirming our calculation that 3 hours is exactly 12.5% of a full day. Why Other Options Are Wrong: 14.9%, 15.6%, 11.4%, and 10% all represent different fractions of a day. For example, 10% of a day would be 2.4 hours, not 3 hours. 15.6% would be more than 3 hours. None of these match the exact fraction 1 / 8 which corresponds to 3 out of 24 hours. Only 12.5% is equivalent to 3 / 24 of the day. Common Pitfalls: Some learners mistakenly divide 24 by 3 instead of forming the ratio 3 / 24, or they calculate the decimal fraction but forget to multiply by 100 to convert to percentage. Others may confuse the base, for example taking 3 as the whole and 24 as the part. Always remember that the percentage is relative to the whole quantity, which in this case is 24 hours. Final Answer: 3 hours is 12.5% of a day.

Question 6

Express 125% as a fraction in simplest form.

Accepted Answer

Introduction / Context: This question checks understanding of converting a percentage into a fraction in simplest form. Knowing how to convert between percentages, fractions, and decimals is a core skill in arithmetic and is frequently used in topics such as ratios, proportions, and probability. Given Data / Assumptions: We are given a percentage: 125%. We must express 125% as a proper or improper fraction in simplest form. No additional context or conditions are needed. Concept / Approach: To convert a percentage to a fraction, we write the percentage as a fraction over 100 and then simplify. For example, X% becomes X / 100. If the resulting fraction is not in simplest form, we reduce it by dividing numerator and denominator by their greatest common divisor. In this problem, 125% will give an improper fraction, which is acceptable as long as it is simplified. Step-by-Step Solution: Step 1: Write 125% as a fraction over 100: 125% = 125 / 100. Step 2: Simplify 125 / 100 by dividing numerator and denominator by 25. Step 3: 125 ÷ 25 = 5 and 100 ÷ 25 = 4, so 125 / 100 simplifies to 5 / 4. Step 4: Check if 5 / 4 can be reduced further. Since 5 and 4 have no common factors other than 1, it is already in simplest form. Step 5: Therefore, 125% as a fraction is 5 / 4. Verification / Alternative check: We can convert 5 / 4 back into a percentage to check. First, express 5 / 4 as a decimal: 5 / 4 = 1.25. Then multiply by 100 to get 1.25 * 100 = 125%. This confirms that the fraction 5 / 4 exactly represents 125%, so the conversion is correct. Why Other Options Are Wrong: 1/4 corresponds to 25%, not 125%. 3/4 corresponds to 75%. 7/4 corresponds to 175%. The option 5/2 corresponds to 250%. None of these equal 125%. Only 5/4 reverses correctly back to 125%, so it is the correct answer. Common Pitfalls: Some learners mistakenly divide 100 by 125 instead of writing 125 / 100, which inverts the fraction. Others convert to a decimal but misplace the decimal point, for example writing 1.25 as 0.125. It is also easy to forget to simplify a fraction such as 125 / 100 before choosing the final answer. Always remember that X% equals X / 100 and then simplify. Final Answer: 125% expressed as a fraction in simplest form is 5/4.

Question 7

An exhibition was conducted for 4 weeks. Compared to the first week, the number of tickets sold in the second week increased by 20%, in the third week increased by 16% over the second week, and in the fourth week decreased by 20% compared to the thi…

Accepted Answer

Introduction / Context: This question deals with successive percentage changes in the number of tickets sold over four weeks of an exhibition. The sales figures change by different percentages each week relative to the previous week. We are given the final week's sales and asked to work backwards to determine the number of tickets sold originally in the first week. This type of problem reinforces understanding of chained percentage multipliers and reverse calculations. Given Data / Assumptions: Let the number of tickets sold in the first week be T. Second week sales = 20% more than first week. Third week sales = 16% more than second week. Fourth week sales = 20% less than third week. Tickets sold in fourth week = 1,392. Concept / Approach: Each weekly change can be expressed as a multiplication factor. A 20% increase corresponds to a factor of 1.20, a 16% increase to 1.16, and a 20% decrease to 0.80. If the first week sales are T, the fourth week sales will be T multiplied sequentially by these factors in order. So Fourth week sales = T * 1.20 * 1.16 * 0.80. We then set this equal to 1392 and solve for T to find the initial sales. Step-by-Step Solution: Step 1: Let first week tickets = T. Step 2: Second week tickets = T increased by 20% = T * 1.20. Step 3: Third week tickets = second week tickets increased by 16% = T * 1.20 * 1.16. Step 4: Fourth week tickets = third week tickets decreased by 20% = T * 1.20 * 1.16 * 0.80. Step 5: We are given that fourth week tickets = 1392, so T * 1.20 * 1.16 * 0.80 = 1392. Step 6: Compute combined multiplier: 1.20 * 1.16 = 1.392. Step 7: Multiply by 0.80: 1.392 * 0.80 = 1.1136. Step 8: Therefore, 1.1136 * T = 1392. Step 9: Solve for T: T = 1392 / 1.1136. Step 10: Compute T: 1392 / 1.1136 = 1250. Step 11: Hence, 1250 tickets were sold in the first week. Verification / Alternative check: Forward check using T = 1250. Second week: 1250 * 1.20 = 1500 tickets. Third week: 1500 * 1.16 = 1740 tickets. Fourth week: 1740 * 0.80 = 1392 tickets. This matches the given fourth week sales exactly, confirming that the initial week sales were correctly computed as 1250 tickets. Why Other Options Are Wrong: If we assume values like 1124, 1420, 1345, or 1300 and apply the same sequence of percentage changes, the resulting fourth week sales will not equal 1392. They will produce either lower or higher values. Only T = 1250, when multiplied by the combined factor 1.1136, gives exactly 1392, so the other options are inconsistent with the described percentage changes. Common Pitfalls: A common error is to treat all percentage changes as relative to the original week instead of successive changes week by week. Another mistake is to add or subtract percentages directly instead of using multiplication factors. Some learners also misapply the 20% decrease by subtracting from the wrong base. Working stepwise and carefully applying each increase or decrease factor in order prevents these problems. Final Answer: The number of tickets sold in the first week was 1,250.

Question 8

There are 600 Kabaddi players. Of them, 4% wear a knee band on one leg only. Of the remaining players, 25% wear knee bands on both legs. How many players do not wear a knee band at all?

Accepted Answer

Introduction / Context: This problem combines percentages and stepwise counting to determine how many players do not use knee bands. It describes a situation where some players wear a band on one leg, some on both legs, and we are asked to find those with none. This is a practical style question that tests careful reading and sequential application of percentage calculations. Given Data / Assumptions: Total number of Kabaddi players = 600. 4% of the players wear a knee band on one leg only. Of the remaining players after removing those with one leg band, 25% wear knee bands on both legs. We must find the number of players who do not wear any knee band. Concept / Approach: First, we compute the number of players with a band on one leg using 4% of the total. We subtract these from the total to get the remaining players. Next, we take 25% of this remaining group as players who wear knee bands on both legs. We then subtract both of these groups from the total to find the players with no band. It is important to note that the 25% is applied to the remaining group, not the original total. Step-by-Step Solution: Step 1: Total players = 600. Step 2: Players with a knee band on one leg = 4% of 600. Step 3: 4% of 600 = 0.04 * 600 = 24 players. Step 4: Remaining players after removing one leg band group = 600 - 24 = 576. Step 5: Of these 576 players, 25% wear bands on both legs. Step 6: Players with bands on both legs = 25% of 576 = 0.25 * 576 = 144. Step 7: Total players with at least one band = players with one leg band + players with both leg bands = 24 + 144 = 168. Step 8: Players with no knee band = Total players - players with at least one band = 600 - 168 = 432. Step 9: Therefore, 432 players do not wear any knee band. Verification / Alternative check: We can check the percentage of players wearing any band. 168 out of 600 players wear at least one knee band, which is 168 / 600 = 0.28 or 28%. That means 72% of players do not wear a knee band. 72% of 600 is 0.72 * 600 = 432, which matches the earlier calculation, confirming that our result is consistent. Why Other Options Are Wrong: 426, 428, 415, and 420 do not match the computed count of 432. If any of these values were used, the implied total number of players with knee bands would not match the given percentages when working backward. Only 432 is consistent with both the 4% and 25% conditions applied in sequence. Common Pitfalls: A frequent mistake is to take 25% of the original 600 instead of the remaining 576 after removing the one leg band players. Another error is to misinterpret the phrase "of the remaining" and simply add 4% and 25% of the total, which leads to incorrect counts. Students may also confuse the number of bands with the number of players; remember that the question is about players, not individual knee bands. Final Answer: The number of players who do not wear a knee band is 432.

Question 9

Which is better: a single discount of 70%, or two successive discounts of 40% and 30% on the marked price?

Accepted Answer

Introduction / Context: This discount problem compares a single large discount with two smaller successive discounts. Many customers and even shopkeepers sometimes get confused about whether two successive discounts are equivalent to a simple sum of the percentages, and whether they match a single large discount. This question helps clarify how successive discounts work and which option gives a lower final price. Given Data / Assumptions: Option 1: A single discount of 70% on the marked price. Option 2: Two successive discounts of 40% and 30% on the same marked price. We assume the same marked price P for fair comparison. We need to determine which option yields a larger discount (that is, lower final price). Concept / Approach: Discounts are applied multiplicatively, not additively. A single discount of 70% means the customer pays 30% of the marked price. Two successive discounts mean we first reduce the price by 40%, then reduce the remaining amount by 30%. To compare, we express the final price as a fraction or percentage of the original marked price P in both cases. The option with the smaller final price is the better discount from the customer perspective. Step-by-Step Solution: Step 1: Let the marked price be P. Step 2: Under a single 70% discount, customer pays 30% of P. Step 3: Final price with 70% discount = 30% of P = 0.30 * P. Step 4: Under successive discounts, first discount is 40%, so new price = 60% of P = 0.60 * P. Step 5: Second discount is 30% on the reduced price, so final price = 70% of 0.60 * P. Step 6: Final price under successive discounts = 0.70 * 0.60 * P = 0.42 * P. Step 7: Compare the final prices: 0.30 * P versus 0.42 * P. Step 8: Clearly, 0.30 * P is less than 0.42 * P, so the single 70% discount gives a lower price. Step 9: Therefore, the 70% discount is better for the buyer. Verification / Alternative check: We can choose a convenient numerical marked price, for example P = 100. For the 70% discount, the customer pays 30% of 100 = 30. For the successive discounts, after 40% discount, price is 60, and then after 30% discount on 60, the customer pays 70% of 60 = 42. Since 30 is less than 42, paying 30 is better from the customer perspective. This simple example confirms that a single 70% discount is more beneficial than successive 40% and 30% discounts. Why Other Options Are Wrong: Saying 40% is better or that both are the same ignores the multiplicative nature of successive discounts. Two discounts of 40% and 30% do not add to 70%; they result in an effective discount of 1 - 0.42 = 58%. Therefore their combined effect is smaller than a single 70% discount. The option "None" and "Depends on the marked price" are incorrect because the comparison holds for any positive marked price, not just specific values. Common Pitfalls: A frequent mistake is to simply add the successive discounts, claiming that 40% + 30% equals 70% and thinking they are equivalent to a single 70% discount. This is incorrect because the second discount is applied to the already reduced price, not the original. Another pitfall is to compare only the discount percentages and not the final paid amounts. Always compute final prices as a fraction of the marked price to make accurate comparisons. Final Answer: A single discount of 70% is better than successive discounts of 40% and 30% on the same marked price.

Question 10

If three eighth of a number is 141, then what is the approximate value of 32.08% of that number?

Accepted Answer

Introduction / Context: This question combines fractions and percentages. First, we are given that three eighth of a number equals 141, and we must find the approximate value of 32.08% of the same number. Such problems are common in aptitude exams and test a student's ability to move comfortably between fraction based information and percentage based requirements. Given Data / Assumptions: Three eighth of a number N is 141. That is, (3 / 8) * N = 141. We must find the approximate value of 32.08% of N. Approximation is allowed, so choosing the closest option is acceptable. Concept / Approach: First, we use the fraction equation (3 / 8) * N = 141 to solve for N. Once we know N, we compute 32.08% of N by converting 32.08% to its decimal form and multiplying by N. Finally, we compare the numeric result to the given options and choose the closest value. This method ensures accurate use of both fractional and percentage information. Step-by-Step Solution: Step 1: Given (3 / 8) * N = 141. Step 2: Solve for N: N = 141 * (8 / 3). Step 3: Compute 141 * 8 = 1128. Step 4: Divide by 3: 1128 / 3 = 376, so N = 376. Step 5: We need 32.08% of N, that is 32.08% of 376. Step 6: Convert 32.08% to decimal: 32.08% = 32.08 / 100 = 0.3208. Step 7: Compute 0.3208 * 376. Step 8: 0.3208 * 376 ≈ 120.6208. Step 9: The approximate value is about 121, but among the given options, 120 is the closest. Verification / Alternative check: We can approximate the percentage slightly. 32.08% is close to 32%. 32% of 376 is 0.32 * 376. Now, 0.32 * 376 = 120.32. This again is close to 120 and consistent with the more exact calculation of about 120.62. So, whether we consider 32% or 32.08%, the nearest integer is around 120, confirming the choice of 120 as the best approximation. Why Other Options Are Wrong: 101, 112, 104, and 130 are either too low or too high compared to 120.62. For example, 112 is around 8 or 9 units away, while 130 overshoots by nearly 9 or 10 units. Among the listed options, 120 is the closest to the computed value of 120.6208, so it is the best approximation and the only correct answer in the context of this question. Common Pitfalls: One common mistake is to solve (3 / 8) * N = 141 incorrectly, for example by multiplying by 3 / 8 instead of 8 / 3 when isolating N. Another pitfall is to misconvert the percentage 32.08% into decimal form, perhaps writing 0.03208 rather than 0.3208. Finally, ignoring the instruction about approximation and expecting an exact match in the options can cause confusion. Always compute carefully and then choose the closest option when approximation is implied. Final Answer: The approximate value of 32.08% of the number is 120.

Question 11

If the price of diesel increases by 25% and Karthik decides that his total spending on diesel can increase by only 15%, by what percentage must he reduce the quantity of diesel he purchases so that his expenditure remains within this new limit?

Accepted Answer

Introduction / Context: In many aptitude and percentage based word problems, the price of a commodity changes and the buyer wants to control or limit the total spending. This question tests the important idea that expenditure is equal to price multiplied by quantity. When the price of diesel increases but Karthik allows his total diesel budget to increase only partly, he must adjust the quantity purchased. Understanding this relation is essential for solving a wide range of exam problems related to inflation, family budgets, and consumption changes. Given Data / Assumptions: Initial diesel price is P per litre. Initial quantity bought is Q litres. Initial expenditure is P * Q. Price increases by 25%, so new price is 1.25 * P. Allowed increase in expenditure is 15%, so new expenditure is 1.15 * P * Q. New quantity purchased is q litres and Karthik wants the new expenditure to match his allowed limit. Concept / Approach: The key concept is that Expenditure = Price * Quantity. When price changes by a certain percentage and expenditure is allowed to change by another percentage, the required percentage change in quantity can be found by equating initial and new expenditure expressions. We find the new quantity as a multiplier of the old quantity, then convert the difference into a percentage reduction. This method avoids trial and error and works for all similar questions in competitive exams. Step-by-Step Solution: Let initial price be P and initial quantity be Q, so initial expenditure is P * Q.Price increases by 25%, so new price becomes 1.25 * P.Allowed expenditure increases by 15%, so new expenditure can be at most 1.15 * P * Q.Let new quantity be q, then new expenditure is 1.25 * P * q.Equate allowed new expenditure and actual new expenditure: 1.25 * P * q = 1.15 * P * Q.Cancel P on both sides to get 1.25 * q = 1.15 * Q, so q = (1.15 / 1.25) * Q = 0.92 * Q.Thus new quantity is 92% of old quantity, so reduction in quantity is 8% of Q. Verification / Alternative check: Assume a simple numerical example for confirmation. Let price initially be Rs 100 per unit and quantity be 1 unit. Initial expenditure is Rs 100. After a 25% increase, new price is Rs 125. If expenditure rises by only 15%, allowed new expenditure is Rs 115. The quantity that can now be bought is 115 / 125, which equals 0.92 units. This matches 92% of the original quantity, confirming that the reduction is 8%. The arithmetic therefore supports the algebraic derivation and confirms the final percentage reduction value. Why Other Options Are Wrong: Option 6.67% is wrong because it would result from incorrect handling of the ratio 1.15 to 1.25. The correct ratio is 0.92, not approximately 0.9333. Option 7.41% is incorrect because it corresponds to a different pair of percentage changes and does not fit the numbers used in this problem. Option 9% is too high, and if used it would give a smaller expenditure than allowed, which does not match the condition that Karthik spends exactly 15% more. Common Pitfalls: A common mistake is to subtract 15 from 25 and assume that quantity must reduce by 10%, which is wrong because expenditure depends on a product of price and quantity, and percentage changes in a product do not combine by simple subtraction. Another typical error is to treat 1.15 / 1.25 as 1.25 / 1.15. Careful attention to which quantity goes in the numerator is crucial. Students should also remember to express the final answer as the percentage reduction, that is the difference between original quantity and new quantity relative to the original quantity, not the remaining percentage of quantity. Final Answer: The required reduction in the quantity of diesel purchased is 8%.

Question 12

Mohan spends fixed percentages of his monthly money on an insurance policy, food, children education, and recreation, and deposits the remaining Rs. 504 in a bank; what total amount does he spend together on food and his insurance policy?

Accepted Answer

Introduction / Context: This problem checks understanding of how to work with percentages of a total amount in practical budget situations. Mohan allocates money to several expense categories and saves the remaining part. From the amount saved, we have to backtrack to the original total amount and then find how much he spends on two particular categories. This type of question is very common in bank exams, SSC, and other aptitude tests where students must reverse percentage calculations. Given Data / Assumptions: Mohan spends 23% of his money on an insurance policy. He spends 33% on food. He spends 19% on children education. He spends 16% on recreation. The remaining amount after these expenses is deposited in a bank. The bank deposit is Rs. 504. Concept / Approach: The total percentage spent on all given expense heads is the sum of the respective percentages. Whatever remains is the unspent percentage, which corresponds to the known rupee amount deposited in the bank. Once we know what percentage corresponds to Rs. 504, we find the total money using a simple reverse percentage step. Finally, we calculate the amount spent on food and insurance policy together by applying their combined percentage to this total amount. This is a standard method of translating percentages into absolute values and vice versa. Step-by-Step Solution: Total percentage spent on all four heads = 23% + 33% + 19% + 16% = 91%.Therefore, percentage left for bank deposit = 100% - 91% = 9%.Bank deposit of Rs. 504 corresponds to 9% of Mohan total money.Let total money be T rupees. Then 9% of T = 504, so 0.09 * T = 504.Thus T = 504 / 0.09 = 5600.Combined percentage for food and insurance policy = 23% + 33% = 56%.So amount spent on food and insurance = 56% of 5600 = 0.56 * 5600 = 3136 rupees. Verification / Alternative check: We can verify by recomputing all allocations from the found total of Rs. 5600. Insurance policy: 23% of 5600 is 1288. Food: 33% of 5600 is 1848. Education: 19% of 5600 is 1064. Recreation: 16% of 5600 is 896. Sum of these expenses is 1288 + 1848 + 1064 + 896 = 5296. Remaining amount is 5600 - 5296 = 304. This looks wrong so recheck the arithmetic. Actually 1288 + 1848 = 3136, and 1064 + 896 = 1960. Then total spent is 3136 + 1960 = 5096, leaving 5600 - 5096 = 504, which matches the given deposit. This confirms that the calculations and result are consistent. Why Other Options Are Wrong: Rs. 2326 is too low and would leave an incorrect remaining amount after considering the other expenses and bank deposit. Rs. 5876 is greater than the total available money, so it is impossible as combined spending on just two categories. Rs. 1741 is not a proper 56% of any nice round total consistent with a deposit of Rs. 504. Common Pitfalls: Students sometimes mistake 504 as 91% instead of 9%, which completely reverses the logic. Another error is to compute 56% of 504 instead of 56% of the total money. Always identify clearly whether a given amount corresponds to a spent percentage or a remaining percentage. Careful reading of the problem statement and recomputation of all percentages are effective ways to avoid such mistakes and verify the result in percentage word problems. Final Answer: The amount Mohan spends on food and insurance policy together is Rs. 3136.

Question 13

When the price of wheat increases by 32% a family adjusts its consumption so that the total expenditure on wheat rises by only 10%; if they earlier consumed 30 kg per month, what is the new monthly wheat consumption of the family?

Accepted Answer

Introduction / Context: This problem focuses on how a change in price and a controlled change in total expenditure affects the quantity of a commodity consumed. It is a classic example of price elasticity style reasoning that appears in aptitude tests. The family faces a price increase for wheat and decides not to let their monthly expenditure grow proportionally, so the only way to achieve this is by reducing the quantity consumed. Given Data / Assumptions: Original monthly consumption of wheat is 30 kg. Original price of wheat is P per kg. Original expenditure is P * 30. Price increases by 32%, so new price is 1.32 * P. New expenditure is only 10% more than before, so it becomes 1.10 times the original expenditure. New quantity consumed is q kg per month, which we need to determine. Concept / Approach: The fundamental relation is Expenditure = Price * Quantity. If both price and expenditure change by different percentages, the quantity must adjust to keep the equality valid. We treat the initial expenditure as a baseline and then relate the new expenditure, price, and quantity with multiplicative factors. Dividing one side by the new price factor gives the new quantity factor, from which we compute the new quantity and finally the reduction in consumption. Step-by-Step Solution: Let initial price be P and original quantity be 30 kg.Original expenditure = P * 30.Price increases by 32%, so new price = 1.32 * P.Expenditure is to increase by only 10%, so new expenditure = 1.10 * (P * 30) = 33 * P.Let new quantity be q kg. Then new expenditure = 1.32 * P * q.Equate the two expressions for new expenditure: 1.32 * P * q = 33 * P.Cancel P to get 1.32 * q = 33, so q = 33 / 1.32 = 25 kg. Verification / Alternative check: Check with actual numbers. Suppose original price P is Rs. 10 per kg. Original consumption is 30 kg, so expenditure is Rs. 300. After price increase, new price is 10 * 1.32 = Rs. 13.2 per kg. New quantity is 25 kg as found. New expenditure = 13.2 * 25 = Rs. 330. This is exactly a 10% increase from Rs. 300 to Rs. 330. Therefore, the answer of 25 kg is consistent and verifies the calculation. Why Other Options Are Wrong: 27 kg would give an expenditure of 27 * 13.2 = 356.4, which is far more than 10% above the original 300. 24 kg gives 24 * 13.2 = 316.8, which is only 5.6% approximately above 300, not the required 10%. 21 kg gives 21 * 13.2 = 277.2, which is actually lower than the original expenditure, contradicting the condition that expenditure increases by 10%. Common Pitfalls: Many learners attempt to subtract percentage changes directly, such as 32% minus 10%, and assume a 22% reduction in quantity. This does not work because the variables are multiplicatively related, not additively. Another common error is to treat the 10% as applied to the new price instead of the overall expenditure. Always define variables carefully, express both old and new expenditure explicitly, and then equate them. Consistent use of percentage multipliers like 1.10 and 1.32 helps avoid arithmetic confusion. Final Answer: The new monthly wheat consumption of the family is 25 kgs.

Question 14

In a class 60% of the students pass in English, 45% pass in Hindi and 25% pass in both subjects; what percentage of students fail in both English and Hindi?

Accepted Answer

Introduction / Context: This problem involves overlapping sets and percentages, a classic topic in quantitative aptitude. It deals with students passing in two different subjects, English and Hindi, and asks for the percentage that fails in both. The question tests understanding of the principle of inclusion and exclusion in the context of percentages instead of absolute numbers, which is very common in competitive exams. Given Data / Assumptions: 60% of the students pass in English. 45% of the students pass in Hindi. 25% of the students pass in both English and Hindi. We assume the total number of students is 100 for convenience, because percentages are involved. We need to determine what percentage fail in both subjects. Concept / Approach: The key concept is the principle of inclusion and exclusion for two sets. For sets A and B, representing passing in English and passing in Hindi, the formula for the percentage of students who pass in at least one subject is: Percentage in A union B = Percentage in A + Percentage in B minus Percentage in intersection of A and B. Once we know the percentage who pass in at least one subject, we subtract that from 100% to find the percentage who fail in both subjects. Step-by-Step Solution: Let the total number of students be 100 for simplicity.Percentage passing in English (E) = 60%.Percentage passing in Hindi (H) = 45%.Percentage passing in both subjects (E and H) = 25%.Using inclusion and exclusion: percentage passing in at least one subject = 60 + 45 - 25 = 80%.Therefore percentage failing in both subjects = 100% - 80% = 20%. Verification / Alternative check: Consider an actual class of 100 students. If 60 pass in English, 45 in Hindi and 25 pass in both, then number who pass only in English is 60 - 25 = 35, and number who pass only in Hindi is 45 - 25 = 20. Students passing in at least one subject are 35 + 20 + 25 = 80. Hence students failing in both are 100 - 80 = 20. The calculation matches the percentage approach exactly, confirming that 20% is the correct value for students who fail in both English and Hindi. Why Other Options Are Wrong: 25% would mean that only 75% pass in at least one subject, which contradicts the computed union of 80% from the formula. 30% would imply that only 70% pass in at least one subject, again inconsistent with the inclusion and exclusion calculation. 15% assumes a smaller failure group than supported by the data and does not satisfy the requirement that the sum of exclusive and overlapping pass groups must equal the known totals. Common Pitfalls: A common mistake is to simply add 60% and 45% and think that 105% is impossible, without subtracting the overlap of 25%. Some learners also subtract the 25% incorrectly or misinterpret it as either only English or only Hindi. To avoid these errors, always draw a simple Venn diagram with two intersecting circles representing English and Hindi, place the 25% in the intersection first and then complete the rest. This visual method reinforces the inclusion and exclusion formula and prevents double counting. Final Answer: The percentage of students who fail in both English and Hindi is 20%.

Question 15

In a class of 80 students and 5 teachers, each student receives shopping coupons equal to 15% of the total number of students and each teacher receives coupons equal to 25% of the total number of students; how many shopping coupons are there in all?

Accepted Answer

Introduction / Context: This problem tests the ability to apply percentage calculations in a combinational situation involving different groups, here students and teachers. Each group receives shopping coupons calculated as a percentage of the total number of students, which may feel unusual at first glance. Such questions train students to read carefully, identify the correct base for each percentage, and then add the contributions from different groups. Given Data / Assumptions: Total number of students = 80. Total number of teachers = 5. Each student gets coupons equal to 15% of the total number of students. Each teacher gets coupons equal to 25% of the total number of students. The total number of coupons is the sum of coupons distributed to all students and all teachers. Concept / Approach: The important point is that the percentage for coupons is calculated on the total number of students, not on the number of people in each group. For students, we first compute how many coupons a single student receives, then multiply by the number of students. We repeat the same for each teacher. Finally, we add both results to get the complete count. Using the total number of students as the base for each percentage is crucial for accuracy. Step-by-Step Solution: Total students = 80, so 15% of total students = 0.15 * 80 = 12.Each student receives 12 coupons.Total coupons for students = 80 * 12 = 960.For teachers, 25% of total students = 0.25 * 80 = 20.Each teacher receives 20 coupons.Total coupons for teachers = 5 * 20 = 100.Combined total coupons = 960 + 100 = 1060. Verification / Alternative check: We can verify using a different view. Consider that there are two types of recipients: 80 students and 5 teachers. Each student gets 12 coupons and each teacher gets 20 coupons. Sum up the coupons for all individuals: for students, 80 times 12 is correct as 8 times 12 is 96 and hence 80 times 12 is 960. For teachers, 5 times 20 is 100. Adding 960 and 100 clearly gives 1060. There is no hidden condition or overlapping count, so this total is reliable. Why Other Options Are Wrong: 960 counts only the coupons given to students and ignores the teachers completely, so it is incomplete. 100 considers only the teachers and leaves out the much larger portion given to students. 1000 is a random intermediate value that does not equal the actual sum of 960 and 100 and therefore does not reflect correct computations. Common Pitfalls: Some students mistakenly take 15% and 25% of the combined total of 85 people instead of taking these percentages of the 80 students. Others also misread the statement and think that each student gets 15 coupons or each teacher gets 25 coupons directly without using any percentage. Carefully identifying the base quantity for percentage calculations and reading phrases like “of the total number of students” are vital skills for avoiding errors in exams. Final Answer: The total number of shopping coupons distributed is 1060.

Question 16

A person purchases 50 mangoes at the same cost price per mango, sells 10 mangoes at a profit of 20%, sells another 20 mangoes at a profit of 30%, and the remaining mangoes get rotten and cannot be sold; what is the overall percentage profit or loss …

Accepted Answer

Introduction / Context: This question explores the concept of overall profit or loss when there are different selling prices for different parts of the same stock and some goods are wasted. In real life and in many exam problems, a seller does not always sell every item at the same profit percentage and some items may be spoiled or unsold. Calculating the combined effect on profit or loss requires careful use of cost price and selling price definitions. Given Data / Assumptions: Total number of mangoes purchased = 50. All mangoes have the same cost price per piece. 10 mangoes are sold at 20% profit. 20 mangoes are sold at 30% profit. The remaining mangoes, which are 20 in number, get rotten and bring zero revenue. We need to find the overall profit or loss percentage on the full lot of 50 mangoes. Concept / Approach: The strategy is to work with a convenient assumed cost price per mango, calculate the total cost price of all mangoes, then compute the total selling price from all sales. The difference between total selling price and total cost price tells us whether there is profit or loss and by how much. Finally, the profit or loss percentage is calculated using the formula: (Profit or Loss / Total Cost Price) * 100. Since the cost per mango is the same, choosing a simple value like Re 1 makes the arithmetic easier without affecting the percentage. Step-by-Step Solution: Assume the cost price per mango is Re 1.Total cost price for 50 mangoes = 50 * 1 = Rs. 50.For 10 mangoes at 20% profit, selling price per mango = 1 * 1.20 = Rs. 1.20.Total selling price for these 10 mangoes = 10 * 1.20 = Rs. 12.For 20 mangoes at 30% profit, selling price per mango = 1 * 1.30 = Rs. 1.30.Total selling price for these 20 mangoes = 20 * 1.30 = Rs. 26.Remaining 20 mangoes are rotten and not sold, so their selling price is zero.Total selling price for all mangoes = 12 + 26 + 0 = Rs. 38.Total cost price is Rs. 50, so loss = 50 - 38 = Rs. 12.Loss percentage = (12 / 50) * 100 = 24% loss. Verification / Alternative check: The assumed cost price could be any convenient value. If we take cost price per mango as Rs. 2 instead, the total cost price becomes Rs. 100. Then selling price for 10 mangoes at 20% profit is 10 * 2.4 = Rs. 24, and for 20 mangoes at 30% profit is 20 * 2.6 = Rs. 52. Total selling price is Rs. 76, while total cost price is Rs. 100, so the loss is still Rs. 24, and the loss percentage is 24 / 100 * 100 = 24%. This confirms that the answer is independent of the assumed cost price value. Why Other Options Are Wrong: 28% loss would require a larger absolute loss relative to the cost, which does not match the calculated difference of Rs. 12 if cost price per mango is Re 1. 26% and 22% loss values similarly do not fit the ratio of 12 to 50, which is exactly 0.24 and not any of those approximations. Common Pitfalls: Some learners wrongly compute separate profit percentages on the quantities sold and then average the percentages, ignoring the unsold rotten mangoes. Others forget that the items that get rotten still contribute to the cost price, even though they bring no revenue. Another typical confusion is whether to divide the net loss by the number of mangoes sold or by the total number purchased. The correct base for the percentage is always the total cost price of all purchased goods in such questions. Final Answer: The transaction results in an overall 24% loss on the mangoes.

Question 17

What is 5% of 4000 rupees expressed as a rupee amount?

Accepted Answer

Introduction / Context: This is a straightforward question on calculating a simple percentage of a given amount. Such problems appear frequently as warm up questions in competitive exams, bank tests, and school level mathematics. Even though the arithmetic is simple, practising these helps improve speed and accuracy that is needed for more complex percentage problems. Given Data / Assumptions: The base amount is 4000 rupees. We are required to find 5% of this amount. The answer must be expressed in rupees. Concept / Approach: The concept is that X% of a number N can be written as (X / 100) * N. Therefore, 5% of 4000 is equal to (5 / 100) times 4000. Another quick mental method is to first find 1% of the number and then multiply by 5. Both methods lead to the same result. Understanding this basic idea is a stepping stone for handling compound percentages and successive increase or decrease problems. Step-by-Step Solution: We need to compute 5% of 4000.Write 5% as a fraction: 5% = 5 / 100.Now calculate (5 / 100) * 4000.Simplify: 5 / 100 = 0.05, so 0.05 * 4000.Compute 0.05 * 4000 = 200.Therefore 5% of 4000 rupees is Rs. 200. Verification / Alternative check: Alternative quick method: find 1% of 4000 first. Since 1% of 4000 is 4000 / 100 = 40, then 5% is five times 1%, which is 5 * 40 = 200. This matches the earlier detailed calculation, confirming that the correct value is Rs. 200. This approach is often faster in timed tests and helps avoid mistakes with decimal multiplication. Why Other Options Are Wrong: Rs. 180 is 4.5% of 4000, not 5%. Rs. 220 is 5.5% of 4000, which is larger than 5% and thus not correct. Rs. 240 is 6% of 4000, again not matching the required 5% of the amount. Common Pitfalls: A frequent error is to misplace the decimal when multiplying by the percentage in decimal form, such as computing 4000 * 0.5 instead of 0.05. Another pitfall is to divide by 5 instead of by 20, confusing 5% with one fifth. Remember that 10% of a number is one tenth of it, and 5% is half of that. Building such mental benchmarks makes percentage calculations much faster and more reliable in all types of exams. Final Answer: 5% of 4000 rupees is Rs. 200.

Question 18

Rohan spends 24% of his money on an insurance policy, 34% on food, 19% on children education and 17% on recreation; the remaining Rs. 540 is deposited in a bank; what total amount does he spend on food and his insurance policy together?

Accepted Answer

Introduction / Context: This problem is similar in structure to many household budget questions where a person divides income into several percentage based heads and saves the rest. We are told the exact amount saved and some spending percentages. The key skill is reversing percentage operations to recover the total income and then calculating how much is spent on particular categories, here food and insurance policy. Given Data / Assumptions: Rohan spends 24% on an insurance policy. He spends 34% on food. He spends 19% on children education. He spends 17% on recreation. The remaining amount deposited in a bank is Rs. 540. We have to find the combined amount spent on food and insurance policy. Concept / Approach: The total percentage spent on the four listed heads is first computed. Whatever remains out of 100% is the percentage that corresponds to the known bank deposit. Once we know that this remaining percentage equals Rs. 540, we find the whole amount using a simple proportion. After recovering the total money, we calculate the combined spending on food and insurance as a fixed percentage of that total. This forward and backward movement between percentages and absolute values is standard in percentage applications. Step-by-Step Solution: Total percentage spent on all given heads = 24% + 34% + 19% + 17% = 94%.Therefore remaining percentage for bank deposit = 100% - 94% = 6%.Given that 6% of Rohan total money equals Rs. 540.Let total money be T rupees. Then 0.06 * T = 540.So T = 540 / 0.06 = 9000 rupees.Combined percentage for food and insurance policy = 34% + 24% = 58%.Amount spent on food and insurance = 0.58 * 9000 = 5220 rupees. Verification / Alternative check: We can verify by reconstructing the entire budget using T = 9000. Insurance policy: 24% of 9000 is 2160. Food: 34% of 9000 is 3060. Education: 19% of 9000 is 1710. Recreation: 17% of 9000 is 1530. Total expenses = 2160 + 3060 + 1710 + 1530 = 8460. Remaining amount is 9000 - 8460 = 540, exactly matching the given bank deposit. Also, the combined amount for insurance and food is 2160 + 3060 = 5220, confirming the result. Why Other Options Are Wrong: Rs. 6350, Rs. 5890 and Rs. 6458 all exceed 58% of 9000 and would leave negative or inconsistent balances when other heads and savings are included. Any of these values would not allow a remaining amount of exactly Rs. 540, so they cannot satisfy all given conditions simultaneously. Common Pitfalls: Some students mistakenly treat Rs. 540 as a part of the spending rather than the leftover savings and compute 94% of some unknown amount as 540. Others add the food and insurance percentages incorrectly or forget to divide by 0.06 correctly. Carefully writing down the formula for the remaining percentage and verifying total allocations at the end is a good practice to avoid these errors. Final Answer: The total amount Rohan spends on food and insurance policy together is Rs. 5220.

Question 19

If A is six times more than B, then by what percentage is B less than A, expressed as a percentage of A?

Accepted Answer

Introduction / Context: Comparisons of quantities using phrases like "times more" and "percent less" often cause confusion. This question tests the understanding of relative comparison from one quantity to another. Here A is described as six times more than B, and we are asked by what percentage B is less than A. The direction of comparison matters a lot, and mixing them up leads to wrong answers even if the numbers are simple. Given Data / Assumptions: A is six times more than B. This phrase is interpreted in arithmetic as A = B + 6B = 7B. We must find by what percentage B is less than A. The percentage must be taken relative to A, because the question asks how much B is less than A. Concept / Approach: The core idea is to translate the verbal description into an equation and then compute the percentage difference. If A is seven times B, then B is only a certain fraction of A. The percentage by which B is less than A can be found by taking the difference A - B and expressing it as a fraction of A, then multiplying by 100. This is different from expressing the difference as a percentage of B, which would answer how much A is more than B instead of how much B is less than A. Step-by-Step Solution: Interpret "A is six times more than B" as A = B + 6B = 7B.Therefore A = 7B.Difference between A and B is A - B = 7B - B = 6B.We need the percentage difference relative to A, so compute (A - B) / A * 100.Substitute A = 7B: (6B) / (7B) * 100.This simplifies to (6 / 7) * 100 which is approximately 85.71%.Thus B is 85.71% less than A when measured as a percentage of A. Verification / Alternative check: Choose a convenient value for B, say B = 100. Then by the given condition, A is six times more than 100, so A = 100 + 6 * 100 = 700. The difference is 700 - 100 = 600. Now find the percentage by which B is less than A. Compute 600 divided by 700, and then multiply by 100: 600 / 700 * 100 = (6 / 7) * 100, which again gives approximately 85.71%. This numeric example confirms the algebraic answer. Why Other Options Are Wrong: 83.33% arises if someone wrongly treats A as 6B instead of 7B. In that mistaken interpretation, difference over A would be (5B) / (6B), which equals 83.33%, but this does not match the phrase "six times more than". 64.82% and 28.56% are arbitrary values that do not correspond to any standard misinterpretation of the phrase and do not match the ratio between A and B as defined. Common Pitfalls: The biggest confusion is between "six times" and "six times more". Many learners read both phrases as A = 6B, but "six times more" mathematically means B plus an additional six times B, that is seven times B. Exam setters sometimes exploit this language issue to test conceptual clarity. It is safer to rewrite such phrases carefully as equations before working with percentages, and always check which quantity is being taken as the base for the percentage calculation. Final Answer: B is 85.71% less than A when expressed as a percentage of A.

Question 20

A man buys a table and a chair together for Rs. 500; he sells the table at a loss of 10% and the chair at a gain of 10% and still makes an overall gain of Rs. 10; what is the cost price of the chair in rupees?

Accepted Answer

Introduction / Context: This question is a classic example of a mixed profit and loss problem involving two items whose combined cost is known. One item is sold at a loss and the other at a gain, and an overall profit is given. From this information, we must determine the individual cost price of one item. Problems like this are common in the profit and loss section of aptitude exams and help train algebraic thinking with percentages. Given Data / Assumptions: Total cost price of a table and a chair together is Rs. 500. The table is sold at a 10% loss. The chair is sold at a 10% profit. The overall gain on the entire transaction is Rs. 10, so the total selling price is Rs. 510. We need to find the cost price of the chair. Concept / Approach: Let the cost price of the table be T and of the chair be C. Then T + C = 500. The selling price of the table is 0.9 * T because of the 10% loss, and the selling price of the chair is 1.1 * C because of the 10% gain. The sum of these two selling prices is 510. This gives a system of two equations in T and C which we solve using basic algebra, then identify the cost price of the chair. This method is systematic and avoids guesswork. Step-by-Step Solution: Let cost price of table be T and cost price of chair be C.We know T + C = 500.Table is sold at 10% loss, so selling price of table = 0.9 * T.Chair is sold at 10% profit, so selling price of chair = 1.1 * C.Overall gain is Rs. 10, so total selling price = 500 + 10 = 510.Therefore 0.9 * T + 1.1 * C = 510.From T + C = 500, express C as 500 - T and substitute.So 0.9 * T + 1.1 * (500 - T) = 510.This simplifies to 0.9T + 550 - 1.1T = 510, giving -0.2T + 550 = 510.Thus -0.2T = -40, so T = 200 and hence C = 500 - 200 = 300. Verification / Alternative check: Using T = 200 and C = 300, compute actual selling prices. Table at 10% loss sells for 200 * 0.9 = 180. Chair at 10% gain sells for 300 * 1.1 = 330. Total selling price is 180 + 330 = 510. Since total cost price is 500, the profit is 510 - 500 = 10, which matches the given data. This confirms that the cost price of the chair is indeed Rs. 300. Why Other Options Are Wrong: If the chair cost were Rs. 200, then table cost would be Rs. 300, and the resulting selling prices would not give an overall profit of exactly Rs. 10. Similarly, chair cost of Rs. 250 or Rs. 400 would break the equation 0.9T + 1.1C = 510 when combined with T + C = 500, leading to either a different net profit or a net loss. Common Pitfalls: Students sometimes misread the phrase "10% loss" and "10% gain" and mistakenly subtract or add 10 rupees directly instead of 10% of the respective cost price. Others assume that equal and opposite percentages automatically cancel, forgetting that the cost prices of the two items are not equal. The safe approach is always to define variables T and C, set up equations for total cost and total selling price, and then solve algebraically. Final Answer: The cost price of the chair is Rs. 300.

Percentage Questions