Question 1

Every month, Kritika spends 30% of her income on house rent and then spends 60% of the remaining amount on household expenditure. If after these expenses she saves ₹ 6300 per month, what is her total monthly income?

Accepted Answer

Introduction / Context: This question deals with successive percentage deductions from an income: first on rent and then on household expenses taken from the remaining balance. The amount left after these deductions represents savings. You are asked to work backwards from the savings to find Kritika's total monthly income. Problems like this test your ability to handle successive percentages and reverse calculations. Given Data / Assumptions: Let Kritika's monthly income be I rupees. She spends 30% of I on house rent. She then spends 60% of the remaining amount on household expenditure. The amount left after these expenses is her monthly savings, equal to ₹ 6300. No other income sources or expenses are mentioned. Concept / Approach: We apply percentages step by step. First, 30% of I is spent on rent, leaving 70% of I. Then, 60% of this remaining 70% is spent on household expenses, leaving 40% of the remaining amount as savings. Therefore, savings equal a fixed fraction of the original income. Once we express savings as a percentage of I, we can set this equal to 6300 and solve for I by simple algebra. Step-by-Step Solution: Step 1: Let monthly income be I. Step 2: Rent = 30% of I = 0.30I. Remaining after rent = I − 0.30I = 0.70I. Step 3: Household expenditure = 60% of the remaining 0.70I = 0.60 * 0.70I = 0.42I. Step 4: Total expenses on rent and household = 0.30I + 0.42I = 0.72I. Step 5: Savings = income − total expenses = I − 0.72I = 0.28I. Step 6: Given savings are ₹ 6300, so 0.28I = 6300. Step 7: Solve for I: I = 6300 / 0.28. Step 8: Compute 6300 / 0.28 = 630000 / 28 = 22,500. Step 9: Therefore, Kritika's monthly income is ₹ 22,500. Verification / Alternative check: Check the calculations using I = ₹ 22,500. Rent = 30% of 22,500 = 0.30 * 22,500 = 6750. Remaining = 22,500 − 6750 = 15,750. Household expenses = 60% of 15,750 = 0.60 * 15,750 = 9450. Total expenses = 6750 + 9450 = 16,200. Savings = 22,500 − 16,200 = 6300, which matches the given savings. Thus, the calculated income is consistent. Why Other Options Are Wrong: ₹ 22,000, ₹ 20,500, ₹ 25,000, and ₹ 18,000: Substituting any of these values into the same calculation results in savings different from ₹ 6300. For example, with ₹ 25,000 income, savings would be 28% of 25,000 = 7000, not 6300. Common Pitfalls: A frequent mistake is to subtract 30% and 60% directly from 100% to conclude that expenses are 90% and savings 10%. This ignores the fact that the 60% is applied to the remaining 70%, not to the original income. Another error is to treat 60% as being calculated on the full income instead of on the remainder. Always apply percentages in the correct order and base them on the amount specified in the problem. Final Answer: Kritika's total monthly income is ₹ 22,500.

Question 2

An article is sold after two successive discounts of 20% and 35% on its marked price. If the final selling price is Rs. 50,700, what is the marked price (in rupees) of the article?

Accepted Answer

Introduction / Context: This question involves successive discounts, a standard topic in percentage based word problems. When more than one discount is applied in sequence, you cannot simply add the percentages; instead, you must apply each discount multiplicatively to the current price. Here, you know the final selling price after two discounts and must work backwards to find the original marked price. Given Data / Assumptions: Let the marked price (MP) be M. First discount = 20% on M. Second discount = 35% on the reduced price after the first discount. Final selling price after both discounts = Rs. 50,700. We must compute M, the original marked price. Concept / Approach: A 20% discount means the buyer pays 80% of the marked price, or 0.80M. Then a 35% discount applied to this reduced price means the buyer pays 65% of that value, or 0.65 * (0.80M). The combined effect is therefore 0.80 * 0.65 = 0.52 of the original marked price. Hence, selling price = 0.52M. We set 0.52M equal to 50,700 and solve for M by simple division. Step-by-Step Solution: Step 1: After the first discount of 20%, the price becomes 80% of M = 0.80M. Step 2: After the second discount of 35%, the price becomes 65% of the reduced price = 0.65 * 0.80M. Step 3: Compute the combined factor: 0.65 * 0.80 = 0.52. Step 4: Therefore, final selling price SP = 0.52M. Step 5: Given that SP = Rs. 50,700, we have 0.52M = 50,700. Step 6: Solve for M: M = 50,700 / 0.52. Step 7: Convert to fraction: 0.52 = 52 / 100, so M = 50,700 * 100 / 52. Step 8: Simplify 50,700 / 52 = 975, so M = 975 * 100 = 97,500. Step 9: Thus, the marked price is Rs. 97,500. Verification / Alternative check: Check by applying both discounts to Rs. 97,500. First discount 20%: discount amount = 0.20 * 97,500 = 19,500. New price after first discount = 97,500 − 19,500 = 78,000. Second discount 35%: discount amount = 0.35 * 78,000 = 27,300. Final selling price = 78,000 − 27,300 = 50,700, which matches the given value. This confirms that the marked price is correctly found. Why Other Options Are Wrong: 92,500; 98,500; 94,000; 90,000: Applying successive discounts of 20% and 35% to any of these values does not result in exactly Rs. 50,700. They correspond to different final prices and therefore do not satisfy the equation 0.52M = 50,700. Common Pitfalls: A common mistake is to add the two discounts directly, claiming that a 20% and 35% discount together make a 55% discount, and then using 45% as the multiplicative factor. This is wrong because the second discount is applied to a reduced price, not the original. Another error is to miscalculate the product of 0.80 and 0.65. Always convert each discount to its remaining fraction (like 0.80 and 0.65) and then multiply them to get the combined factor. Final Answer: The marked price of the article is Rs. 97,500.

Question 3

20% of a man's salary is paid as house rent, 60% is spent on his living expenses and 10% represents his savings. If he spends the remaining Rs. 30 on the education of his children, what is his total monthly salary?

Accepted Answer

Introduction / Context: This question tests your understanding of percentage allocation of income along with a small fixed amount spent on an extra category. The man's salary is divided into percentages for rent, living expenses, and savings, and the remaining part is given as a specific rupee amount for education. You must use these pieces of information to recover the total salary. Given Data / Assumptions: Let the man's salary be S rupees. 20% of S is spent on house rent. 60% of S is spent on living expenses. 10% of S is saved. The remaining amount, spent on children's education, equals Rs. 30. All percentages are based on the total salary S. Concept / Approach: First, we note that 20% + 60% + 10% = 90% of the salary is accounted for by rent, living expenses, and savings. The remaining part of the salary is 10% (because 100% − 90% = 10%). We are told that this remaining part is Rs. 30, so 10% of S equals 30. This directly allows us to solve for S using a simple percentage equation. Step-by-Step Solution: Step 1: Total salary = S. Step 2: Percentages: 20% for rent, 60% for living, 10% for savings. Total accounted percentage = 20% + 60% + 10% = 90%. Step 3: Remaining percentage of salary = 100% − 90% = 10%. Step 4: This remaining 10% of S is spent on education, and is given to be Rs. 30. Step 5: Write the equation: 10% of S = 30, or (10 / 100) * S = 30. Step 6: Simplify: 0.10S = 30. Step 7: Solve for S: S = 30 / 0.10 = 300. Step 8: Therefore, the man's monthly salary is Rs. 300. Verification / Alternative check: Check that the distribution matches the problem statement for S = 300. Rent = 20% of 300 = 0.20 * 300 = 60. Living expenses = 60% of 300 = 0.60 * 300 = 180. Savings = 10% of 300 = 30. Total of these three = 60 + 180 + 30 = 270. Remaining amount for education = 300 − 270 = 30, which matches the given figure. Thus the salary of Rs. 300 is consistent. Why Other Options Are Wrong: 900, 3000, 9000, 600: For each of these salary values, 10% would not equal 30. For example, 10% of 900 is 90, and 10% of 3000 is 300, both of which conflict with the given information that the remaining amount is Rs. 30. Common Pitfalls: Some students incorrectly try to calculate each category in rupees first without setting up a clear equation, which can lead to confusion. Others treat the Rs. 30 as an additional percentage value instead of a fixed remainder. The simplest and safest method is to observe that the percentages sum to 90% and then directly equate the remaining 10% to 30. Final Answer: The man's total monthly salary is Rs. 300.

Question 4

A man's average monthly expenditure for the first four months of a year is Rs. 231.25. For the next five months, his average monthly expenditure is Rs. 22.75 more than this first average. He spends a total of Rs. 605 during the last three months of …

Accepted Answer

Introduction / Context: This question combines average calculations, total expenditure over different periods, and percentage savings. You are given monthly averages for two blocks of months and a total amount for the remaining months, along with the man's annual income. The task is to compute how much of that income is saved, expressed as a percentage. This tests multi step reasoning, careful handling of averages, and percentage interpretation. Given Data / Assumptions: Average monthly expenditure for first 4 months = Rs. 231.25. Average monthly expenditure for next 5 months is Rs. 22.75 more than 231.25. Total expenditure in last 3 months = Rs. 605. Annual income = Rs. 3500. There are 12 months in the year, divided into 4 + 5 + 3 months as provided. We must find (total savings / annual income) * 100. Concept / Approach: First, use the average for the first 4 months to find total expenditure in that block. Then, compute the new average for the next 5 months by adding Rs. 22.75 to the original average, and multiply by 5 to get total expenditure for those months. Add the known total for the last 3 months to obtain total annual expenditure. Finally, subtract this total expenditure from the annual income to find savings, and convert this to a percentage of the annual income. Step-by-Step Solution: Step 1: Total expenditure in the first 4 months = average * number of months = 231.25 * 4. Step 2: Compute 231.25 * 4 = (231 * 4) + (0.25 * 4) = 924 + 1 = Rs. 925. Step 3: Average in the next 5 months = 231.25 + 22.75 = Rs. 254. Step 4: Total expenditure in the next 5 months = 254 * 5 = Rs. 1270. Step 5: Total expenditure in the last 3 months is given as Rs. 605. Step 6: Total annual expenditure = 925 + 1270 + 605. Step 7: Compute 925 + 1270 = 2195; then 2195 + 605 = Rs. 2800. Step 8: Annual income = Rs. 3500, so total savings = 3500 − 2800 = Rs. 700. Step 9: Percentage of income saved = (savings / income) * 100 = (700 / 3500) * 100. Step 10: Simplify 700 / 3500 = 1 / 5 = 0.20, so savings percentage = 0.20 * 100 = 20%. Verification / Alternative check: We can quickly re check: total expenditure 2800 plus total savings 700 equals the income 3500, so the numbers are internally consistent. Also, saving 1/5 of the income corresponds to 20%, which matches our final calculation. No month is left out: 4 + 5 + 3 = 12 months are fully accounted for. Why Other Options Are Wrong: 10%: Would mean savings of 350, giving total expenditure of 3150, which contradicts the computed 2800. 15%: Implies savings of 525 and expenditure of 2975, not matching any of the given blockwise totals. 25%: Implies savings of 875, leading to total expenditure 2625, which is inconsistent with 925 + 1270 + 605. 5%: Corresponds to savings of only 175, which conflicts even more strongly with the calculated expenditures. Common Pitfalls: A frequent mistake is to confuse the average increase for the next five months with an additional monthly amount on top of the yearly average, or to miscalculate the total for each block by simplifying 231.25 incorrectly. Another common error is forgetting to add all three blocks correctly before subtracting from income. Always compute each block total separately, check the month counts, and then add them up before working out the savings percentage. Final Answer: The man saves 20% of his annual income during the year.

Question 5

A sum of Rs. 2600 is lent out in two parts: one part at 9% simple interest per annum and the other part at 7% simple interest per annum. If the total annual interest from both parts together is Rs. 206, how much money was lent at 7%?

Accepted Answer

Introduction / Context: This is a classic simple interest and linear equation problem. A fixed total amount is split between two different interest rates, and the total annual interest is known. You are asked to find how much of the principal was invested at the lower rate. Such questions test your ability to form and solve linear equations involving percentages. Given Data / Assumptions: Total principal lent = Rs. 2600. Part of the money is lent at 9% simple interest per annum. The remaining part is lent at 7% simple interest per annum. Total annual interest (from both parts together) = Rs. 206. We must find the amount lent at 7%. Interest is simple and calculated for one year. Concept / Approach: Let the amount lent at 9% be x. Then the amount lent at 7% is 2600 − x. The annual simple interest from a principal P at rate R% is (P * R / 100). Using this, we write expressions for interest from each part and add them to match the given total interest of Rs. 206. This gives a linear equation in x, which can be solved by basic algebra. After finding x, we subtract it from 2600 to get the amount at 7%. Step-by-Step Solution: Step 1: Let the amount lent at 9% be x rupees. Step 2: Then the amount lent at 7% is 2600 − x rupees. Step 3: Annual interest from the 9% part = x * 9 / 100 = 0.09x. Step 4: Annual interest from the 7% part = (2600 − x) * 7 / 100 = 0.07(2600 − x). Step 5: Total annual interest = 0.09x + 0.07(2600 − x) = 206. Step 6: Expand: 0.09x + 0.07 * 2600 − 0.07x = 206. Step 7: Compute 0.07 * 2600 = 182. Step 8: Combine like terms: (0.09x − 0.07x) + 182 = 206 ⇒ 0.02x + 182 = 206. Step 9: Subtract 182 from both sides: 0.02x = 24. Step 10: Solve for x: x = 24 / 0.02 = 1200. Step 11: Amount lent at 7% = 2600 − 1200 = 1400. Verification / Alternative check: Check interest values for Rs. 1200 at 9% and Rs. 1400 at 7%. Interest from 1200 at 9% = 1200 * 9 / 100 = 108. Interest from 1400 at 7% = 1400 * 7 / 100 = 98. Total interest = 108 + 98 = 206, which matches the given total. Thus the split is verified, and Rs. 1400 is correctly identified as the amount lent at 7%. Why Other Options Are Wrong: Rs. 900, Rs. 1600, Rs. 1200, Rs. 1000: Substituting any of these values as the 7% part leads to total interest values different from Rs. 206. For example, if 1600 were lent at 7%, the remaining 1000 at 9% would produce 112 + 112 = 224 in interest, not 206. Common Pitfalls: Students sometimes mistakenly assign x to the 7% part instead of the 9% part and then misinterpret the final result. Another common error is in handling the signs when expanding 0.07(2600 − x), especially forgetting the negative sign in front of 0.07x. Carefully forming the equation and checking each expansion step helps avoid these mistakes. Final Answer: The amount of money lent at 7% is Rs. 1400.

Question 6

In an election between two candidates, 70% of the enrolled voters cast their votes. Out of the votes cast, 2% were declared invalid. One candidate received 7203 votes, which was 60% of the total valid votes. What was the total number of voters enrol…

Accepted Answer

Introduction / Context: This question combines several percentage concepts in the context of an election: turnout, invalid votes, and a candidate's share of valid votes. You are given the number of votes obtained by one candidate and the percentages at each stage, and you must work backwards to find the total number of voters enrolled. This tests multi step percentage reasoning and careful algebra. Given Data / Assumptions: Let the total number of enrolled voters be T. 70% of T cast their votes, so total votes cast = 70% of T. 2% of the votes cast are invalid. Therefore 98% of the votes cast are valid. One candidate receives 7203 votes, which is 60% of the valid votes. We must find T. Concept / Approach: Work backwards from the candidate's votes. If 7203 is 60% of the valid votes, then valid votes = 7203 / 0.60. Once we know the number of valid votes, we can find total votes cast by recognizing that valid votes are 98% of votes cast. Then, knowing that votes cast are 70% of total enrolled voters, we can find T. This stepwise reverse calculation is typical in layered percentage problems. Step-by-Step Solution: Step 1: Let V be total valid votes. Step 2: Candidate's votes = 60% of V = 0.60V = 7203. Step 3: Solve for V: V = 7203 / 0.60. Step 4: 0.60 = 3/5, so V = 7203 * (5 / 3). Step 5: Compute 7203 / 3 = 2401, then multiply by 5: V = 2401 * 5 = 12,005 valid votes. Step 6: Let C be total votes cast. Valid votes are 98% of C, so 0.98C = 12,005. Step 7: Solve for C: C = 12,005 / 0.98. Step 8: 0.98 = 98 / 100, so C = 12,005 * 100 / 98 = 12,005 * (50 / 49). Step 9: Compute 12,005 / 49 = 245, then multiply by 50: C = 245 * 50 = 12,250 votes cast. Step 10: Votes cast are 70% of total voters T, so 0.70T = 12,250. Step 11: Solve for T: T = 12,250 / 0.70 = 12,250 * (10 / 7) = 17,500. Verification / Alternative check: Check the entire chain with T = 17,500. Votes cast = 70% of 17,500 = 0.70 * 17,500 = 12,250. Invalid votes = 2% of 12,250 = 0.02 * 12,250 = 245. Valid votes = 12,250 − 245 = 12,005. Candidate's votes = 60% of 12,005 = 0.60 * 12,005 = 7203. All figures match the problem statement, confirming T = 17,500. Why Other Options Are Wrong: 18,050; 17,000; 7,203; 20,000: Using any of these values as T leads to a different number of votes cast, valid votes, and candidate votes, which will not match 7203 under the given percentages. For example, if T were 17,000, votes cast would be 11,900, leading to different valid votes and a different 60% value. Common Pitfalls: Some students mistakenly apply 2% invalid to total voters rather than to votes cast, while others use 60% of total votes instead of valid votes. Another frequent error is trying to jump directly from 7203 to T in one step without carefully tracking each percentage stage. It is safer to proceed step by step: candidate votes → valid votes → votes cast → total voters. Final Answer: The total number of voters enrolled in the election was 17,500.

Question 7

In a school, 75 pupils appeared for an examination and 80% of them passed. Another school sent 10 more pupils than the first school, and 5 fewer pupils passed than in the first school. What was the pass percentage in the second school?

Accepted Answer

Introduction / Context: This problem compares examination performance in two schools using numbers of pupils and pass percentages. The first school's data is given directly, and the second school's information is given relative to the first. You must determine the pass percentage for the second school. This tests your ability to convert between absolute numbers and percentages and to reason across two related scenarios. Given Data / Assumptions: First school: 75 pupils appeared, and 80% passed. Second school: number of pupils who appeared is 10 more than the first school. Number of pupils who passed in the second school is 5 less than in the first school. We must find the pass percentage in the second school. All pupils either pass or fail; there are no other categories. Concept / Approach: First, compute the number of pupils who passed in the first school using 80% of 75. Then use the given relations to find both the number of pupils who appeared and the number who passed in the second school. Finally, compute the pass percentage in the second school as (passed / appeared) * 100. Converting everything into actual counts before finding the percentage keeps the reasoning clear. Step-by-Step Solution: Step 1: First school: pupils appeared = 75. Step 2: Pass count in first school = 80% of 75. Step 3: Compute 80% of 75: (80 / 100) * 75 = 0.8 * 75 = 60. So 60 pupils passed in the first school. Step 4: Second school: pupils appeared = 10 more than 75 = 75 + 10 = 85. Step 5: Pupils passed in second school = 5 fewer than in first school = 60 − 5 = 55. Step 6: Pass percentage in second school = (55 / 85) * 100. Step 7: Simplify the fraction 55 / 85 = 11 / 17. Step 8: Compute (11 / 17) * 100 ≈ 64.705..., which is usually written as 64.7% (approx). Verification / Alternative check: We can check the reasonableness: in the first school, 60 out of 75 passed, giving 80%. In the second school, more students appeared (85), but fewer passed (55), so the pass percentage must be lower than 80%. Our result of about 64.7% is indeed less than 80%, and when reversed, 64.7% of 85 is approximately 55, consistent with the given data. Why Other Options Are Wrong: 75%: Would correspond to about 63.75 passing out of 85, which does not match the actual 55 passes. 84% and 72%: Both are higher than 64.7%, and using them would produce pass counts significantly different from 55 when multiplied by 85. 68%: Closer but still higher than the correct value; 68% of 85 is 57.8, not 55. Common Pitfalls: Some students mistakenly take 80% of 85 or misread the relationship about 5 fewer passes. Others compute the pass percentage by subtracting 5 from 80 directly, which incorrectly mixes absolute counts and percentages. Always convert percentages to actual student counts in each school and then recompute the percentage for the second school from those counts. Final Answer: The pass percentage in the second school is approximately 64.7%.

Question 8

A candidate scores 45% of the total marks in an examination but still falls short of the pass mark by 40 marks. If the pass percentage is 55%, what are the maximum possible marks in the exam?

Accepted Answer

Introduction / Context: This question tests the core percentage concept of relating a candidate's obtained marks, pass percentage, and maximum marks in an examination. It is a very common aptitude pattern where the difference between two percentages of the same total is given as an absolute number of marks. Learning to convert such information into a simple linear equation helps in quickly finding the maximum marks and is very useful for competitive exams. Given Data / Assumptions: The candidate scores 45% of the total marks. The pass percentage for the exam is 55% of the total marks. The candidate fails by 40 marks, which means the pass marks are 40 more than the candidate's marks. We assume a single exam with a fixed maximum mark M. Concept / Approach: The key idea is that both the candidate's marks and the pass marks are percentages of the same maximum marks M. The difference between 55% and 45% is 10% of M. This 10% of M is numerically equal to 40 marks. Once we know that 10% corresponds to 40, we can scale up to find 100% of the total marks. Step-by-Step Solution: Let the maximum marks in the exam be M.Candidate's marks = 45% of M = 45/100 * M.Pass marks = 55% of M = 55/100 * M.Given that the candidate fails by 40 marks, so 55/100 * M − 45/100 * M = 40.This simplifies to (10/100) * M = 40.So 0.10 * M = 40, hence M = 40 / 0.10 = 400. Verification / Alternative check: If the maximum marks are 400, then 45% of 400 is 0.45 * 400 = 180 marks. The pass marks are 55% of 400, which is 0.55 * 400 = 220 marks. The difference between 220 and 180 is 40 marks, which exactly matches the statement that the candidate fails by 40 marks. This confirms that 400 is correct. Why Other Options Are Wrong: 300: Ten percent of 300 is 30, so the difference between 45% and 55% would be 30 marks, not 40. 350: Ten percent of 350 is 35, so the shortfall would be 35 marks, which does not match the given 40 marks. 450: Ten percent of 450 is 45, so the shortfall would become 45 marks, not 40. 550: Ten percent of 550 is 55, again inconsistent with the given difference of 40 marks. Common Pitfalls: Students sometimes directly take 10% of the candidate's marks instead of 10% of the total marks, which is incorrect. Another common mistake is to subtract 45 from 55 and treat 10 as marks instead of a percentage. It is also easy to mix up pass percentage with pass marks. Always remember that both percentages act on the same unknown total M, so the difference in percentages multiplied by M gives the mark difference. Final Answer: The maximum possible marks in the exam are 400.

Question 9

The simple interest on a principal of Rs 400 for 10 years amounts to Rs 280. What is the annual rate of simple interest (per annum) charged by the lender?

Accepted Answer

Introduction / Context: This question checks your understanding of simple interest, one of the most basic and frequently tested topics in aptitude exams. You are given the principal amount, the time in years, and the total simple interest earned. From this, you must determine the annual rate of interest. It is a direct formula-based question and is ideal for practicing percentage and interest calculations. Given Data / Assumptions: Principal P = Rs 400. Time T = 10 years. Simple interest SI = Rs 280. Rate of interest per annum is R% and needs to be found. The interest is simple interest, not compound interest. Concept / Approach: The standard simple interest formula is SI = (P * R * T) / 100. When simple interest, principal, and time are known, we can rearrange this formula to find the rate R. This involves basic algebra and careful substitution of the values given in the question. Once R is computed, we interpret it as a percentage per annum. Step-by-Step Solution: Use the formula SI = (P * R * T) / 100.Substitute the known values: 280 = (400 * R * 10) / 100.Simplify the right-hand side: (400 * 10) / 100 = 40, so 280 = 40 * R.Solve for R: R = 280 / 40.Compute the division: R = 7.Therefore, the rate of interest per annum is 7%. Verification / Alternative check: We can verify by recalculating the simple interest using R = 7%. Using SI = (400 * 7 * 10) / 100, we get SI = (400 * 70) / 100 = 28000 / 100 = 280. This exactly matches the given simple interest amount, confirming that the rate is correct. Why Other Options Are Wrong: 8%: At 8%, SI would be (400 * 8 * 10) / 100 = 320, which is higher than 280. 5%: At 5%, SI would be (400 * 5 * 10) / 100 = 200, which is less than 280. 6%: At 6%, SI would be (400 * 6 * 10) / 100 = 240, still less than 280. 7.5%: At 7.5%, SI would be (400 * 7.5 * 10) / 100 = 300, which does not match the given interest. Common Pitfalls: Learners sometimes forget to divide by 100 in the formula or mix up the relationship between rate and time. Another error is to miscalculate the multiplication 400 * 10 or to mistakenly treat 10 years as 10 months. To avoid mistakes, always write the formula clearly, substitute values systematically, and simplify gradually instead of doing all steps mentally. Final Answer: The annual rate of simple interest is 7%.

Question 10

By selling 175 pineapples, a fruit seller earns a profit that is exactly equal to the selling price of 50 pineapples. What is the percentage gain made by the seller on each pineapple?

Accepted Answer

Introduction / Context: This problem involves profit percentage and requires you to interpret a verbal condition relating total profit to the selling price of a certain number of items. Such questions are common in profit and loss topics in aptitude exams and help you understand how to translate real-world statements into algebraic equations. Given Data / Assumptions: The seller sells 175 pineapples. Total profit earned is equal to the selling price of 50 pineapples. Cost price per pineapple is assumed to be the same for all pineapples. Selling price per pineapple is also the same for all pineapples. Concept / Approach: The key idea is to use variables for cost price and selling price per pineapple and then use the relationship between total profit and selling price. If cost price per pineapple is C and selling price per pineapple is S, then total profit on 175 pineapples is (S − C) * 175. The question states that this profit equals the selling price of 50 pineapples, that is 50 * S. Solving this equation gives the ratio S/C, and from that we can compute profit percentage. Step-by-Step Solution: Let cost price per pineapple be C and selling price per pineapple be S.Total selling price of 175 pineapples = 175 * S.Total cost price of 175 pineapples = 175 * C.Total profit on 175 pineapples = 175 * S − 175 * C = 175 * (S − C).Given that this profit equals selling price of 50 pineapples, so 175 * (S − C) = 50 * S.Expand and rearrange: 175S − 175C = 50S, so 125S = 175C.Therefore S / C = 175 / 125 = 7 / 5.Profit per pineapple = S − C = (7/5)C − C = (2/5)C.Profit percentage = (Profit / Cost price) * 100 = (2/5) * 100 = 40%. Verification / Alternative check: Assume a convenient cost price to verify, for example C = Rs 5. Then S = (7/5) * 5 = Rs 7. Profit per pineapple is Rs 2. Profit on 175 pineapples is 175 * 2 = Rs 350. Selling price of 50 pineapples is 50 * 7 = Rs 350. Both match perfectly, confirming that a 40% profit is correct. Why Other Options Are Wrong: 32%: This would correspond to a smaller ratio between S and C that does not satisfy the given equality between profit and selling price of 50 pineapples. 28% and 30%: Both represent lower profit margins, and if used to compute S / C, they will not make the profit on 175 items equal to the selling price of 50 items. 35%: Also does not satisfy the specific algebraic relationship derived from the condition in the question. Common Pitfalls: Many students confuse total profit with profit percentage and may incorrectly equate 175 to 50 or directly attempt a shortcut without forming an equation. Another error is to assume cost price is 1 and mis-handle fractions. The safest approach is always to introduce variables, write down the profit expression clearly, and then solve systematically for S/C. Final Answer: The seller's gain percentage is 40%.

Question 11

Three students A, B and C appear in an examination. A scores 18% more marks than B and 12% fewer marks than C. If B scores 220 marks, how many marks does C score in the same exam?

Accepted Answer

Introduction / Context: This question combines percentage increase and decrease in the context of examination marks. You are given relational information about how much more A scores than B and how much less A scores than C. Such problems are very common in aptitude tests under the percentage or ratio category and help develop flexibility in handling linked percentage relationships. Given Data / Assumptions: B scores 220 marks. A scores 18% more than B. A scores 12% less than C. All marks are from the same examination and are comparable. Concept / Approach: The approach is to first express A's marks in terms of B using the 18% increase. Then, use the information that A's marks are 12% less than C to link A and C. If A is 12% less than C, then A is 88% of C or 0.88 * C. Setting the two expressions for A equal allows us to solve for C. Step-by-Step Solution: Marks of B = 220.A scores 18% more than B, so A = 220 + 18% of 220.Compute 18% of 220: 18/100 * 220 = 39.6.Therefore, A = 220 + 39.6 = 259.6 marks.A scores 12% less than C, so A = 88% of C = 0.88 * C.So we have 0.88 * C = 259.6.Hence, C = 259.6 / 0.88.Compute C: 259.6 / 0.88 = 295. Verification / Alternative check: We can verify this value of C. If C = 295, then 12% of 295 is 0.12 * 295 = 35.4. Subtracting this from 295 gives 295 − 35.4 = 259.6, which matches A's marks. Also, check A relative to B: B has 220, and A has 259.6, which is 39.6 more. The percentage increase is 39.6 / 220 * 100 = 18%, confirming the consistency. Why Other Options Are Wrong: 245: If C were 245, then 12% less than 245 would be 245 − 29.4 = 215.6, which does not match A's marks. 230: Twelve percent less than 230 is 202.4, again not compatible with an 18% increase from B's 220 marks. 224: Similarly, 12% less than 224 is 197.12, which is too low and inconsistent with the data. 260: If C were 260, 12% less would be 228.8, which does not produce the correct relationship to B. Common Pitfalls: A frequent mistake is to treat 18% more and 12% less with respect to the wrong base, such as applying both directly on B or C. Another typical error is to subtract percentages directly instead of forming algebraic equations. Always express each relationship carefully in equation form and keep track of which percent relates to which student. Final Answer: C scores 295 marks.

Question 12

A shopkeeper gives two successive discounts of 20% and 30% on the marked price of an article. What is the single equivalent discount percentage on the article?

Accepted Answer

Introduction / Context: This question checks your understanding of successive discounts, a standard topic under percentage and profit and loss. Many shoppers and exam candidates mistakenly add discounts directly, but in reality each discount is applied on the reduced price, not on the original price. You are asked to find the net or equivalent single discount. Given Data / Assumptions: First discount = 20% on the marked price. Second discount = 30% on the already reduced price. There is one marked price for the article. We need the single discount that gives the same final selling price. Concept / Approach: When two successive discounts are given, we multiply the remaining price factors. A 20% discount leaves 80% of the price, which is a factor 0.80. A 30% discount leaves 70% of the price, or factor 0.70. The combined factor is 0.80 * 0.70. The net discount is 1 minus this combined factor, converted to a percentage. Step-by-Step Solution: Let the marked price be M.After a 20% discount, the price becomes 80% of M, so price = 0.80 * M.On this reduced price, a second discount of 30% is given, leaving 70% of the reduced price.New price = 0.70 * (0.80 * M) = 0.56 * M.Thus the customer finally pays 56% of the marked price.Net discount percentage = (1 − 0.56) * 100 = 0.44 * 100 = 44%. Verification / Alternative check: Assume a simple marked price, say M = Rs 100. After a 20% discount, price becomes Rs 80. After a further 30% discount, price becomes 70% of 80, which is 0.70 * 80 = Rs 56. The overall discount from Rs 100 is Rs 44, that is 44%. This numeric check supports the earlier factor method. Why Other Options Are Wrong: 40%: This is simply 20% + 20% (a miscalculation) or sometimes guessed incorrectly. It ignores the compounding effect. 56%: This would imply the customer pays only 44% of the price, but we computed that they pay 56% of the price, not the other way round. 50%: This is just an average and has no mathematical basis in the given situation. 60%: This is clearly too high compared to giving 20% and 30% sequentially. Common Pitfalls: A very common error is to directly add the discounts (20% + 30% = 50%) and claim 50% as the net discount. However, the second discount is taken on the already reduced price, so the base changes. Another mistake is to confuse the fraction of price remaining with the discount itself. Always convert each discount into a remaining percentage factor and multiply them to get the final paid percentage. Final Answer: The net equivalent discount is 44%.

Question 13

An article is sold for Rs 16896 after two successive discounts of 20% and 12% are applied on its marked price. What is the marked price of the article in rupees?

Accepted Answer

Introduction / Context: This question extends the idea of successive discounts. Instead of asking for the net discount, it gives the final selling price after discounts and asks you to recover the marked price. These reverse percentage problems are common in competitive exams and require careful handling of discount factors. Given Data / Assumptions: First discount = 20% on the marked price. Second discount = 12% on the already reduced price. Final selling price after both discounts = Rs 16896. We need to find the original marked price M. Concept / Approach: Each discount reduces the price by a certain factor. A 20% discount leaves 80% of the price, which is a factor 0.80. A 12% discount leaves 88% of the price, which is a factor 0.88. Multiplying these factors gives the fraction of the marked price that the customer actually pays. Then we set this fraction of M equal to the final selling price and solve for M. Step-by-Step Solution: Let the marked price be M.After a 20% discount, price becomes 80% of M = 0.80 * M.After a 12% discount on this reduced price, the price becomes 88% of the reduced amount.So final price = 0.88 * (0.80 * M) = 0.704 * M.Given that this final price is Rs 16896, we have 0.704 * M = 16896.Therefore, M = 16896 / 0.704.Compute M: 16896 / 0.704 = 24000. Verification / Alternative check: Check using the found marked price. If M = Rs 24000, then after a 20% discount the price is 80% of 24000, which is Rs 19200. After a further 12% discount, the price becomes 88% of 19200, that is 0.88 * 19200 = Rs 16896. This matches the given selling price exactly, so the marked price is confirmed. Why Other Options Are Wrong: 22000 and 21500: When you apply 20% and 12% discounts on these values, the final price is lower than 16896. 23800: The final price after both discounts will be slightly below the required 16896. 20000: After successive discounts, this would give a final price much lower than 16896. Common Pitfalls: The most frequent mistake is to subtract 20% and 12% directly from the marked price or to treat the total discount as 32%. Another error is to divide the selling price by incorrect factors, such as 0.68 or 0.80 alone. Always remember that successive discounts multiply as factors, and reverse problems require you to divide by the combined factor to get back to the original price. Final Answer: The marked price of the article is Rs 24000.

Question 14

While buying a dress on sale, a person spends Rs 45 and saves Rs 5 due to the discount. What is the percentage of savings with respect to the original marked price?

Accepted Answer

Introduction / Context: This problem is a straightforward application of percentage on a real-life discount situation. The shopper pays a reduced amount and is told how much money is saved. You are required to express this saving as a percentage of the original price, which is a common scenario in sales and marketing questions. Given Data / Assumptions: Amount paid after discount = Rs 45. Amount saved due to discount = Rs 5. Original marked price is the sum of amount paid and amount saved. We need to find savings percentage relative to the original price. Concept / Approach: The original marked price is equal to the amount actually paid plus the amount saved, because without discount the buyer would have paid the full price. Once the original price is found, the saving percentage is calculated as (saving / original price) * 100. This is a direct percentage formula question. Step-by-Step Solution: Amount paid after discount = Rs 45.Amount saved = Rs 5.Original marked price = paid amount + saved amount.So original price = 45 + 5 = Rs 50.Saving percentage = (saving / original price) * 100.Saving percentage = (5 / 50) * 100 = 10%. Verification / Alternative check: We can think of it this way: If the original price is Rs 50 and the shopper saves Rs 5, then the person is paying Rs 45, which is 90% of the original price. Therefore, the discount is 10% of the original price. This reasoning aligns with the calculated saving percentage. Why Other Options Are Wrong: 5%: This would correspond to a saving of Rs 2.5 on Rs 50 or some similar small fraction, which does not match the actual saving of Rs 5. 12% or 15%: These percentages would require a different ratio between saving and original price. For example, 15% discount on Rs 50 would mean a saving of Rs 7.5, which is not correct here. 20%: A 20% saving on Rs 50 would be Rs 10, which is double the actual saving. Common Pitfalls: Some students mistakenly calculate the percentage of saving based on the amount paid (5 out of 45) instead of the original price, which leads to an incorrect answer. Others may try to guess the percentage without computing the original price. Always identify what the percentage is based on, and remember that discounts are normally calculated on the marked price. Final Answer: The percentage of savings with respect to the original price is 10%.

Question 15

Two litres of pure alcohol are added to 6 litres of a solution that contains 40% alcohol and 60% water. After mixing, what is the percentage of water in the final 8 litre solution?

Accepted Answer

Introduction / Context: This problem belongs to the topic of mixtures and alligation, framed here using percentages. It tests your ability to separate components of a solution, add another component, and then recompute the percentage of one constituent, in this case water. Such mixture questions appear frequently in quantitative aptitude exams. Given Data / Assumptions: Initial solution volume = 6 litres. Initial solution has 40% alcohol and 60% water. Pure alcohol added = 2 litres. Total final volume after mixing = 6 + 2 = 8 litres. We need the percentage of water in the final solution. Concept / Approach: The key approach is to separately track the quantities of alcohol and water. In the original solution, the water and alcohol amounts can be found using their percentages. When pure alcohol is added, only the alcohol quantity increases, while water stays the same. After finding the new total volumes of alcohol and water, we compute the new water percentage as (water volume / total volume) * 100. Step-by-Step Solution: Initial solution volume = 6 litres, with 40% alcohol and 60% water.Quantity of alcohol initially = 40% of 6 = 0.40 * 6 = 2.4 litres.Quantity of water initially = 60% of 6 = 0.60 * 6 = 3.6 litres.Pure alcohol added = 2 litres. This increases only the alcohol content.New alcohol quantity = 2.4 + 2 = 4.4 litres.Water quantity remains 3.6 litres.Total volume of solution after mixing = 8 litres.Percentage of water in final solution = (3.6 / 8) * 100 = 45%. Verification / Alternative check: We can cross-check arithmetic: 3.6 divided by 8 equals 0.45. Multiplying by 100 gives 45%. Also, the alcohol percentage would be 55%, because 4.4 / 8 = 0.55, and 45% + 55% = 100%. This consistency check confirms that the water percentage is correctly calculated. Why Other Options Are Wrong: 55%: This is actually the alcohol percentage, not the water percentage, in the final mixture. 60% and 65%: These values would imply that the water portion increased or did not change, which is impossible because additional alcohol was added but no extra water was added. 50%: This would correspond to equal quantities of water and alcohol, which does not match the computed values. Common Pitfalls: One common mistake is to take the average of 40% and some assumed higher value without considering volumes. Another error is to forget that water quantity stays constant when pure alcohol is added. Some students incorrectly assume that the original 60% water remains 60% in the final solution. Always recompute based on actual quantities rather than relying on mental shortcuts. Final Answer: The percentage of water in the final solution is 45%.

Question 16

Three students A, B and C appear in an examination. A scores 36% fewer marks than B and 16% more marks than C. If B scores 145 marks, how many marks does C score?

Accepted Answer

Introduction / Context: This question again focuses on percentage relationships between the marks of three students. It combines a percentage decrease relationship between A and B and a percentage increase relationship between A and C. These kinds of problems help you understand how to move between values when given relative percentage comparisons. Given Data / Assumptions: B scores 145 marks. A scores 36% less than B. A scores 16% more than C. All marks are from the same test and are comparable. Concept / Approach: We first compute A's marks using the fact that A scores 36% less than B, so A is 64% of B. Then we use the relation that A is 16% more than C, which means A is 116% of C or 1.16 * C. By equating these two expressions for A, we can solve for C. This process converts the verbal relationships into a solvable equation. Step-by-Step Solution: Marks of B = 145.A scores 36% less than B, so A = 64% of B.Therefore, A = 64/100 * 145.Compute 64 * 145 = 9280, so A = 9280 / 100 = 92.8 marks.A scores 16% more than C, so A = 116% of C = 1.16 * C.Hence, 1.16 * C = 92.8.So C = 92.8 / 1.16.Compute C: 92.8 / 1.16 = 80. Verification / Alternative check: Check with C = 80. A is 16% more than C, so A = 80 + 16% of 80 = 80 + 12.8 = 92.8, which matches our value for A. Now B should be such that A is 36% less than B. If B = 145, then 36% of 145 is 52.2, and B − 36% of B = 145 − 52.2 = 92.8. This matches A again, so the relationships are consistent. Why Other Options Are Wrong: 120 and 110: These are larger than 92.8, so A could not be 16% more than C if C were this large. 75: If C were 75, then A as 16% more than C would be 87, which does not fit with the computed 92.8. 90: Similarly gives A = 90 + 16% of 90 = 104.4, which is too large compared to 92.8. Common Pitfalls: A frequent mistake is reversing the direction of the percentage change, for example treating 36% less as 64% more or misreading 16% more than C as C being 16% more than A. Another common error is computing percentages using approximations and rounding too early, which can distort the result. Carefully set up each relationship using the correct base value. Final Answer: C scores 80 marks.

Question 17

During a sale, a shop announces a 40% discount on the marked price of Rs 1000 for a product, but a customer finally buys it for Rs 510. What additional discount percentage (over and above the announced 40% on the marked price) did the customer effec…

Accepted Answer

Introduction / Context: This question involves interpreting discounts in two stages. First, there is an announced discount on the marked price, and then there is an additional price reduction leading to an even lower selling price. You are asked to compute how much extra discount, as a percentage of the already reduced sale price, the customer obtained beyond the advertised discount. Given Data / Assumptions: Marked price of the product = Rs 1000. Announced discount = 40% on the marked price. Expected sale price after 40% discount = 60% of 1000. Actual selling price to the customer = Rs 510. We must find the additional discount percentage on the price after the 40% discount. Concept / Approach: The first step is to compute the normal discounted price with a 40% reduction. Then, compare this intended sale price with the actual price paid. The difference between these two amounts is the extra discount. Since the question asks for additional discount, we interpret it as a percentage of the price after the 40% discount, not again on the original marked price. Step-by-Step Solution: Marked price = Rs 1000.A 40% discount means the customer should normally pay 60% of the marked price.Expected price after 40% discount = 60% of 1000 = 0.60 * 1000 = Rs 600.Actual selling price is Rs 510.Extra reduction in rupees = 600 − 510 = Rs 90.Additional discount percentage (over the reduced price) = (90 / 600) * 100.Compute (90 / 600) * 100 = (0.15) * 100 = 15%. Verification / Alternative check: We can also calculate the total discount directly from the marked price. Total discount = 1000 − 510 = Rs 490. Total discount percentage on marked price = 490 / 1000 * 100 = 49%. The announced discount was 40%. The difference between total discount (49%) and announced discount (40%) is 9%. However, this 9% is relative to the marked price, not the extra discount relative to the reduced sale price. The question explicitly talks about additional discount after the 40% reduction, which we correctly computed as 15% based on the Rs 600 price. Why Other Options Are Wrong: 10%: If the extra discount were 10% of Rs 600, the reduction would be Rs 60, leading to a price of Rs 540, not Rs 510. 25% and 30%: These would imply much larger reductions from Rs 600, giving prices lower than Rs 510. 20%: An extra 20% on Rs 600 would be Rs 120, so the price would drop to Rs 480, which is not the actual selling price. Common Pitfalls: Many students mistakenly compute the difference between 49% and 40% as 9% and treat that as the answer. This ignores that the extra discount is usually interpreted as a percentage of the price after the first discount, not of the original price. Always clarify which base you are using for the percentage, especially when phrases like additional discount or extra discount are used. Final Answer: The additional discount over the already reduced sale price is 15%.

Question 18

A shop offers a deal in which 1 shirt is given free on the purchase of 4 shirts of the same price. What is the effective discount percentage on each shirt due to this offer?

Accepted Answer

Introduction / Context: This question presents a common promotional scheme: buy a certain number of items and get one free. You need to convert this type of offer into an equivalent percentage discount. Such questions are standard in profit and loss and percentage topics and help in understanding effective discounts in real-world offers. Given Data / Assumptions: The offer is: buy 4 shirts and get 1 shirt free. All shirts have the same marked price. The buyer ultimately receives 5 shirts but pays only for 4 shirts. We need the effective discount percentage per shirt. Concept / Approach: Let the marked price of each shirt be P. Under the offer, the customer gets 5 shirts but pays 4P. The effective price per shirt is total amount paid divided by number of shirts received. The effective discount percentage is then computed by comparing this effective price per shirt with the original marked price P. Step-by-Step Solution: Let the marked price of one shirt be P.Without any offer, paying for 5 shirts would cost 5P.Under the scheme, the customer pays only for 4 shirts and receives 5 shirts.Total amount paid = 4P, total shirts received = 5.Effective price per shirt = 4P / 5 = 0.8P.Discount per shirt = original price − effective price = P − 0.8P = 0.2P.Effective discount percentage = (0.2P / P) * 100 = 20%. Verification / Alternative check: Assume a simple numerical price, say P = Rs 100. Without any offer, 5 shirts would cost Rs 500. With the offer, the customer pays 4 * 100 = Rs 400 and receives 5 shirts. Effective price per shirt = 400 / 5 = Rs 80. The discount per shirt is 100 − 80 = Rs 20, which is 20% of 100. This confirms the 20% effective discount. Why Other Options Are Wrong: 25%: This would imply paying Rs 75 per Rs 100 shirt, which does not match the computed Rs 80 effective price. 16% or 24%: These values correspond to different ratios between amount paid and items received; they are not consistent with a 4-for-5 scheme. 30%: This would mean a much larger reduction than the actual effect of the offer. Common Pitfalls: Students sometimes treat 1 free out of 5 as 20% of the number of shirts and directly state the discount as 20% without checking if it matches the price calculation. While in this case it coincidentally matches, it is safer to compute using the total amount paid and total quantity received. This approach generalises more reliably to similar but slightly different offers. Final Answer: The effective discount on each shirt is 20%.

Question 19

If 35% of (x + y) is equal to 40% of (x − y), then x is what percentage of y?

Accepted Answer

Introduction / Context: This is an algebraic percentage problem involving two variables x and y. You are given an equation where percentages of sums and differences of x and y are equal, and you need to express x as a percentage of y. This type of problem mixes percentages with basic algebra and is often seen in algebra and percentage sections of aptitude tests. Given Data / Assumptions: 35% of (x + y) equals 40% of (x − y). The variables x and y are real numbers and y is nonzero so that the percentage comparison makes sense. We must find how many percent x is of y. Concept / Approach: First, we convert the percentage statement into an equation using decimal or fractional equivalents. Then, we simplify the equation to get a relationship between x and y. Once we express x in terms of y, we convert the ratio x / y into a percentage by multiplying by 100. The key is to carefully distribute and combine like terms. Step-by-Step Solution: Given: 35% of (x + y) = 40% of (x − y).Write percentages as fractions: 35/100 * (x + y) = 40/100 * (x − y).Multiply both sides by 100 to remove denominators: 35(x + y) = 40(x − y).Expand both sides: 35x + 35y = 40x − 40y.Rearrange to group x terms and y terms: 35y + 40y = 40x − 35x.So 75y = 5x.Hence x = (75y) / 5 = 15y.Therefore, x / y = 15, so x is 15 times y. In percentage form, x is 15 * 100% = 1500% of y. Verification / Alternative check: To verify, choose a convenient value for y, for example y = 1. Then x = 15 * 1 = 15. Now compute both sides of the original statement. Left side: 35% of (x + y) = 35% of (15 + 1) = 35% of 16 = 0.35 * 16 = 5.6. Right side: 40% of (x − y) = 40% of (15 − 1) = 40% of 14 = 0.40 * 14 = 5.6. Both sides are equal, confirming the relationship. Why Other Options Are Wrong: 150% and 200%: These would imply that x is only slightly larger than y, which contradicts the derived equation x = 15y. 105%: This is just a little more than y and clearly does not satisfy the algebraic relationship when tested. 15%: This would imply x is smaller than y, again inconsistent with x being 15 times y. Common Pitfalls: Common mistakes include cancelling incorrectly, forgetting to distribute the percentages across both x and y terms, or directly equating coefficients without expanding properly. Another error is misinterpreting 15 as 15% instead of 1500%. Always remember that if x = ky, then x as a percentage of y is k * 100%, not just k. Final Answer: The value of x is 1500% of y.

Question 20

If the radius of a circle is increased by 15%, by what percentage does the area of the circle increase?

Accepted Answer

Introduction / Context: This question links percentage change in a geometric measurement (radius) to the resulting change in area. It tests your understanding that area of a circle depends on the square of the radius. A percentage increase in radius does not produce the same percentage increase in area; instead, the effect is amplified due to the square relationship. Given Data / Assumptions: The radius of a circle is increased by 15%. The original radius is r and the new radius is 1.15 * r. Area of a circle is proportional to the square of its radius. We must find the percentage increase in area. Concept / Approach: The area of a circle is A = pi * r^2. If the radius changes to r_new, the new area becomes pi * r_new^2. The ratio of new area to old area is (r_new^2) / (r^2). When the radius is multiplied by 1.15, the area is multiplied by (1.15)^2. The percentage increase in area is then (area factor − 1) * 100. Step-by-Step Solution: Let the original radius be r.Original area A1 = pi * r^2.Radius is increased by 15%, so new radius = 1.15 * r.New area A2 = pi * (1.15 * r)^2.Compute the square: (1.15 * r)^2 = 1.15^2 * r^2 = 1.3225 * r^2.So A2 = pi * 1.3225 * r^2 = 1.3225 * A1.Area increase factor = 1.3225, so percentage increase = (1.3225 − 1) * 100.Percentage increase = 0.3225 * 100 = 32.25%. Verification / Alternative check: To verify, take an example. Suppose the original radius is 10 units. Then original area is proportional to 10^2 = 100 units squared. New radius is 11.5 units, and area is proportional to 11.5^2 = 132.25 units squared. Increase in area = 132.25 − 100 = 32.25 units squared. Percentage increase = 32.25 / 100 * 100 = 32.25%. This confirms the calculation. Why Other Options Are Wrong: 30%: This is close but ignores the exact effect of squaring 1.15. 16.125%: This is roughly half of the correct value and might come from incorrectly applying the percentage to only one factor. 25% and 15%: These treat the change in radius and area as if they are directly proportional, which is not correct because area depends on the square of the radius. Common Pitfalls: A typical mistake is to assume that the percentage change in area equals the percentage change in radius. Another error is to compute 15% of the area and add it once, ignoring the square effect. Always remember that when a dimension is squared in a formula, percentage changes must be handled by applying the change factor and then squaring it, not by squaring the percentage itself. Final Answer: The area of the circle increases by 32.25%.

Percentage Questions