Question 1

Company workforce after attrition: A company has 724 employees. If 25% of them leave, how many employees remain?

Accepted Answer

Introduction / Context: This is a straightforward percentage decrease problem: remove 25% of a total to find the remaining headcount. Given Data / Assumptions: Total employees initially = 724. Percentage leaving = 25%. Remaining percentage = 75% of the original. Concept / Approach: Remaining = Initial * (1 − 0.25) = Initial * 0.75. Step-by-Step Solution: Compute 75% of 724.0.75 * 724 = 543.0.Therefore, 543 employees remain. Verification / Alternative check: 25% of 724 = 181 (since 724/4 = 181). Subtract: 724 − 181 = 543. Why Other Options Are Wrong: 550, 578, 565, 600 are not equal to 724 * 0.75. Common Pitfalls: Computing the number who left and forgetting to subtract from the original total, or rounding prematurely (here the value is exact). Final Answer: 543

Question 2

Commission calculation on sales: An agent sells goods worth ₹15000. If the commission rate is 12 1/2%, how much commission does the agent earn?

Accepted Answer

Introduction / Context: We compute sales commission based on a percentage of the sale value. Here, 12 1/2% is a friendly fraction for mental math. Given Data / Assumptions: Sales value = ₹15000. Commission rate = 12 1/2% = 12.5% = 1/8. Concept / Approach: Commission = Rate * Sale amount. Using 1/8 simplifies calculation. Step-by-Step Solution: Commission = (1/8) * 15000.= 15000 / 8 = 1875.So the commission is ₹1875. Verification / Alternative check: Compute as 12.5%: 0.125 * 15000 = 1875 — same result. Why Other Options Are Wrong: ₹2125, ₹2000, ₹2700, ₹1750 do not equal 12.5% of ₹15000. Common Pitfalls: Converting 12 1/2% incorrectly. Always remember 12 1/2% = 1/8 = 0.125. Final Answer: ₹1875

Question 3

Price markdown effect: An article costs ₹15000. Due to a market slump, its price decreases by 8%. What is the new price?

Accepted Answer

Introduction / Context: This question applies a single percentage decrease to a marked price to find the new price after a discount-like reduction. Given Data / Assumptions: Original price = ₹15000. Decrease = 8%. Concept / Approach: New price = Original * (1 − decrease%). Here that factor is 0.92. Step-by-Step Solution: New price = 15000 * 0.92.= 15000 − 8% of 15000.8% of 15000 = 0.08 * 15000 = 1200.New price = 15000 − 1200 = ₹13800. Verification / Alternative check: Calculate directly: 15000 * 0.92 = 13800 — consistent. Why Other Options Are Wrong: ₹14000, ₹16500, ₹12600, ₹13200 are not equal to 92% of ₹15000. Common Pitfalls: Subtracting 8 rupees or 8% of a different base. Always compute 8% of the original price. Final Answer: ₹13800

Question 4

Successive changes on money in hand: A person loses 20% of his money. He then spends 25% of the remainder and is left with ₹480. What amount did he originally have?

Accepted Answer

Introduction / Context: This problem uses successive percentage changes on an unknown amount. The final remainder is given, and we work backward to the original sum. Given Data / Assumptions: Original amount = X. After losing 20%, remainder = 80% of X = 0.8X. He then spends 25% of this remainder, so he keeps 75% of it. Final amount left = ₹480. Concept / Approach: Apply successive multipliers: Final = X * 0.8 * 0.75. Solve for X using the given final amount. Step-by-Step Solution: Final amount = X * 0.8 * 0.75 = X * 0.60.0.60X = 480.X = 480 / 0.60 = 800. Verification / Alternative check: Check forward: Start 800 ⇒ after −20% ⇒ 640 ⇒ spend 25% of 640 (which is 160) ⇒ left 480. Works perfectly. Why Other Options Are Wrong: ₹600, ₹720, ₹840, ₹1000 do not produce ₹480 after the given successive changes. Common Pitfalls: Adding or subtracting percentages arithmetically instead of using multiplicative factors for successive changes. Final Answer: ₹800

Question 5

Evaluate a chained percent–fraction expression: Compute 12 × 26% × (5/78) × 38% × (7/152) × 10000.

Accepted Answer

Introduction / Context: This computation chains percentages and fractions with a final multiplication by 10000. Converting percents to decimals and simplifying stepwise keeps arithmetic clean. Given Data / Assumptions: Expression: 12 * (26/100) * (5/78) * (38/100) * (7/152) * 10000. All operations are multiplications; order can be regrouped for easier cancellation. Concept / Approach: Convert percents to fractions, then cancel common factors before multiplying. Look for simplifications like 10000 with denominators 100 and 152/78 factors. Step-by-Step Solution: Rewrite: 12 * (26/100) * (5/78) * (38/100) * (7/152) * 10000.First, combine the percent denominators with 10000: (100 * 100) in denominator cancels to 100 with 10000, leaving a factor 100.Now compute (7/152) * 100 = 700/152 = 25 * (28/152) = 25 * (7/38) = 175/38.Multiply remaining fractions: (26 * 5 * 38) / 78 = (26 * 5 * 38) / (2 * 39).Since 38 = 2 * 19 and 26 = 2 * 13, numerator = (2*13)*5*(2*19) = 4 * 13 * 5 * 19; divide by 2 in denominator ⇒ 2 * 13 * 5 * 19 / 39.39 = 3 * 13; cancel 13 ⇒ (2 * 5 * 19) / 3 = 190/3.Now: 12 * (190/3) * (175/38) = 4 * 190 * (175/38) (since 12/3 = 4).4 * 190 = 760. Then 760 * 175 / 38 = (760/38) * 175 = 20 * 175 = 3500.Finally divide by remaining 100 from earlier percent handling → 3500 / 100 = 35. Verification / Alternative check: Numerical evaluation with decimals also yields 35 (e.g., 0.26 * 0.38 * 12 * 10000 * 5/78 * 7/152). Why Other Options Are Wrong: 38, 41, 52, 28 are distractors near the true value but not equal to the exact simplification 35. Common Pitfalls: Forgetting to convert percents to fractions, or mismanaging cancellations with 10000 leading to a factor-of-10 error. Final Answer: 35

Question 6

Compare relative performance: Shantanu's marks are 40% less than Kamal's. By what percent are Kamal's marks greater than Shantanu's?

Accepted Answer

Introduction / Context: This problem flips a percentage comparison. If one value is 40% less than another, the reverse comparison produces a larger-than-40% increase due to the smaller base. Given Data / Assumptions: Let Kamal's marks = K. Shantanu's marks = 60% of K = 0.6K. We seek the percent by which K exceeds 0.6K. Concept / Approach: Percent increase from Shantanu to Kamal = (K − 0.6K) / 0.6K * 100%. Step-by-Step Solution: Difference = 0.4K.Relative to Shantanu: 0.4K / 0.6K = 2/3.Percent = (2/3) * 100% = 66 2/3 %. Verification / Alternative check: Pick K = 100: then Shantanu = 60. Increase from 60 to 100 is 40 on a base of 60, i.e., 40/60 = 66.666…%. Why Other Options Are Wrong: 33 1/3 % and 44 3/5 % come from misplacing the base. 55 2/3 % underestimates the true ratio. 60% equates to the original difference relative to the larger base, not the smaller. Common Pitfalls: Using 40% directly for the reverse comparison; always compute relative to the smaller base when asked “how much more than Shantanu.” Final Answer: 66 2/3 %

Question 7

Revenue impact of simultaneous decreases: Due to low rainfall, the land price drops by 12% and its production falls by 4%. What is the overall percentage change in revenue (price × production)?

Accepted Answer

Introduction / Context: Revenue equals price multiplied by quantity. When both price and output change, multiply their factors to get total revenue change. Given Data / Assumptions: Price decrease = 12% ⇒ factor = 0.88. Production decrease = 4% ⇒ factor = 0.96. Revenue factor = 0.88 * 0.96. Concept / Approach: Overall percentage change = (combined factor − 1) * 100%. Product of factors captures simultaneous effects. Step-by-Step Solution: Revenue factor = 0.88 * 0.96 = 0.8448.Percentage change = (0.8448 − 1) * 100% = −15.52%.Hence, revenue falls by 15.52%. Verification / Alternative check: Use the approximation formula: net % ≈ −12% + −4% + (−12%)*(−4%)/100 = −16% + 0.48% = −15.52%, exactly matching. Why Other Options Are Wrong: Loss of 16% ignores the positive cross-term. Gains are impossible since both factors fell. Loss of 12.48% is an arbitrary mismatch. Common Pitfalls: Adding percentage changes directly without the interaction term; simultaneous changes require multiplying factors. Final Answer: Loss of 15.52%

Question 8

Markup followed by discount: A shopkeeper marks goods 20% above cost price and later allows a 5% discount on the marked price. What is the net profit or loss percent?

Accepted Answer

Introduction / Context: This problem uses successive percentage changes on price: first an increase (markup), then a decrease (discount). The combined effect determines profit or loss relative to cost price. Given Data / Assumptions: Cost Price (CP) = 100 (assumed for ease). Markup = +20% ⇒ Marked Price (MP) = 120. Discount = 5% on MP ⇒ Selling Price (SP) = 120 * 0.95. Concept / Approach: Compute SP after both operations. Profit % = (SP − CP) / CP * 100%. Step-by-Step Solution: SP = 120 * 0.95 = 114.Profit = 114 − 100 = 14.Profit % = 14/100 * 100% = 14%. Verification / Alternative check: Use factors: net factor = 1.20 * 0.95 = 1.14 ⇒ 14% profit directly. Why Other Options Are Wrong: All others mismatch the exact net factor 1.14. Common Pitfalls: Subtracting 5% from 20% to get 15% profit; discounts apply on the increased base, so you must multiply factors. Final Answer: 14% (profit)

Question 9

Maintain expenditure amid price rise: If the price of sugar rises by 25%, by what percentage must a family reduce consumption to keep its sugar expense unchanged?

Accepted Answer

Introduction / Context: Another inverse-percentage adjustment: to keep spending the same when price increases, consumption must drop in the inverse ratio. Given Data / Assumptions: Price increase r = 25%. Expenditure = Price * Quantity remains constant. Concept / Approach: Required decrease = r/(100 + r) * 100%. Step-by-Step Solution: Decrease = 25 / 125 * 100%.= 1/5 * 100% = 20%. Verification / Alternative check: Assume initial price 100, quantity 1 ⇒ spend 100. New price 125. New quantity for same spend = 100/125 = 0.8 ⇒ 20% reduction. Why Other Options Are Wrong: 21% and 22% are close but incorrect; exact math gives 20%. 25% would overcompensate. Common Pitfalls: Subtracting 25 percentage points from quantity without using the inverse ratio. Final Answer: 20%

Question 10

Price drop with constant expenditure: If the price of tea decreases by 6%, by what percent must consumption increase to keep total spending unchanged?

Accepted Answer

Introduction / Context: When price falls, more can be bought for the same money. The increase needed is not simply 6%; it must offset the 6% price drop exactly. Given Data / Assumptions: Price decrease r = 6%. Expenditure must remain the same. Concept / Approach: If price multiplies by (1 − r), consumption must multiply by 1/(1 − r). Required percentage increase = [1/(1 − r) − 1] * 100% = r/(1 − r) * 100%. Step-by-Step Solution: r = 0.06 ⇒ Required increase = 0.06 / 0.94 * 100%.= (6/94) * 100% = (3/47) * 100%.3/47 as a mixed percent = 6 18/47% (since 0.063829… = 6.3829…%). Verification / Alternative check: Assume initial price 100, quantity 1 ⇒ spend 100. New price 94. New quantity Q requires 94Q = 100 ⇒ Q = 100/94 = 1.063829… ⇒ 6.3829…% increase = 6 18/47%. Why Other Options Are Wrong: 5 16/47%, 6 17/47% are off by small fractions. 4 18/67% is unrelated. 6% would leave a slight shortfall in expenditure. Common Pitfalls: Adding 6% instead of using the inverse factor; exact compensation requires r/(1 − r), not r alone. Final Answer: 6 18/47%

Question 11

Passing threshold from fail data: A student must score 40% to pass. He scores 40 marks and fails by 40 marks. What are the maximum marks of the exam?

Accepted Answer

Introduction / Context: We will use the relationship between required pass percentage, maximum marks, and the student’s shortfall. Given Data / Assumptions: Pass mark = 40% of maximum marks M. Student’s actual marks = 40. He fails by 40 marks ⇒ Pass mark = 40 + 40 = 80. Concept / Approach: Set 0.40 * M = 80 and solve for M. Step-by-Step Solution: 0.40M = 80.M = 80 / 0.40 = 200. Verification / Alternative check: 40% of 200 = 80. Candidate had 40, short by 40 — matches the statement. Why Other Options Are Wrong: 250, 300, 150, 400 do not yield a pass mark of 80 at 40%. Common Pitfalls: Confusing “fails by 40” with “scored 40%” or misplacing what the 40 refers to. Final Answer: 200

Question 12

Two candidates around the pass mark: One candidate scores 20% and fails by 50 marks. Another scores 40% and gets 30 marks more than the minimum required. Find the maximum marks of the exam.

Accepted Answer

Introduction / Context: This problem frames two conditions around the pass mark. We express both in terms of the unknown maximum marks and solve simultaneously. Given Data / Assumptions: Maximum marks = M; Pass mark = P. Candidate A: 20% of M is 50 below P ⇒ 0.2M + 50 = P. Candidate B: 40% of M is 30 above P ⇒ 0.4M = P + 30. Concept / Approach: Equate the two expressions for P from each condition to eliminate P and solve for M. Step-by-Step Solution: From A: P = 0.2M + 50.From B: P = 0.4M − 30.Equate: 0.2M + 50 = 0.4M − 30 ⇒ 0.2M = 80 ⇒ M = 400. Verification / Alternative check: Compute P from either equation: P = 0.2*400 + 50 = 80 + 50 = 130. Check B: 40% of 400 = 160, which is 30 more than 130 — consistent. Why Other Options Are Wrong: 500, 450, 300, 350 do not satisfy both conditions simultaneously. Common Pitfalls: Misreading “fails by 50” and “gets 30 more than minimum” or mixing up which is percent of what. Final Answer: 400

Question 13

Population with opposite successive changes: Town population = 126800. It increases by 15% in the first year and decreases by 20% in the second year. What is the population after 2 years?

Accepted Answer

Introduction / Context: Successive percent changes multiply, not add. We apply the 15% increase then the 20% decrease to the base 126800. Given Data / Assumptions: Initial population = 126800. Year 1 factor = 1.15. Year 2 factor = 0.80. Concept / Approach: Final population = 126800 * 1.15 * 0.80 = 126800 * 0.92. Step-by-Step Solution: Compute 126800 * 0.92.126800 * 92/100 = (1268 * 92) = 116656.Therefore, population after 2 years = 116656. Verification / Alternative check: Increase by 15%: 126800 → 145820; then decrease by 20%: 145820 * 0.8 = 116656. Both methods agree. Why Other Options Are Wrong: Other values do not match the exact factor 0.92 applied to 126800. Common Pitfalls: Adding −20% and +15% to get −5% and multiplying once; this ignores compounding on different bases. Final Answer: 116656

Question 14

Future population with annual compounding: A town has 705600 people. If population grows at 5% per annum, what will it be after 2 years?

Accepted Answer

Introduction / Context: We compute a 2-year compound increase at 5% per year. This is a direct application of compound growth. Given Data / Assumptions: P0 = 705600. Annual rate r = 5% = 0.05. Years n = 2. Concept / Approach: Population after 2 years: P = P0 * (1 + r)^n = 705600 * 1.05^2 = 705600 * 1.1025. Step-by-Step Solution: 1.05^2 = 1.1025.P = 705600 * 1.1025 = 705600 + 0.1025 * 705600.0.1025 * 705600 = 72324.Total = 705600 + 72324 = 777924. Verification / Alternative check: Compute 5% of 705600 = 35280; add to get year 1 (740880). Then 5% of 740880 = 37044; year 2 total = 740880 + 37044 = 777924. Why Other Options Are Wrong: The other numbers are near but not equal to 705600 * 1.1025. Common Pitfalls: Multiplying by 1.10 (simple 10% total) instead of 1.1025; compounding matters. Final Answer: 777924

Question 15

Back-calculating past population: The current population is 1058400 and grows at 5% per annum. What was the population 2 years ago?

Accepted Answer

Introduction / Context: Given the present population and a known annual growth rate, we reverse compound to find the population two years earlier. Given Data / Assumptions: P_now = 1058400. Annual rate r = 5%. We need P_past such that P_now = P_past * (1.05)^2. Concept / Approach: P_past = P_now / (1.05^2) = 1058400 / 1.1025. Step-by-Step Solution: Compute 1058400 / 1.1025.Observation: 960000 * 1.1025 = 960000 + 0.1025 * 960000 = 960000 + 98400 = 1058400.Thus P_past = 960000. Verification / Alternative check: Exact multiplication confirms the reverse calculation without long division. Why Other Options Are Wrong: Other figures do not yield 1058400 when multiplied by 1.1025. Common Pitfalls: Subtracting 10% once (linear thinking) instead of reversing compound growth. Final Answer: 960000

Question 16

Compute growth amount (not final total): A city has population 250000, increasing at 2% per year. What is the increase in population after 2 years (growth amount only)?

Accepted Answer

Introduction / Context: We are asked for the increase (difference between the 2-year future population and the original), not the final population itself. Given Data / Assumptions: P0 = 250000. Annual rate r = 2%. Years n = 2. Concept / Approach: Increase = P0 * [(1 + r)^n − 1] = 250000 * (1.02^2 − 1). Step-by-Step Solution: 1.02^2 = 1.0404.Increase factor = 1.0404 − 1 = 0.0404.Increase amount = 250000 * 0.0404 = 10100. Verification / Alternative check: Year 1 increase: 2% of 250000 = 5000 ⇒ total 255000. Year 2 increase: 2% of 255000 = 5100. Total increase over two years = 5000 + 5100 = 10100. Why Other Options Are Wrong: 2500 and 5000 count only a single year or half. 10000 ignores compounding in the second year. 252000 is a total population distractor, not the increase. Common Pitfalls: Multiplying 2% by 2 without compounding; this underestimates the growth by 100. Final Answer: 10100

Question 17

Boys to girls ratio from a percent relation: In a school, 10% of the boys equals one-fourth of the girls. What is the ratio of boys to girls?

Accepted Answer

Introduction / Context: We translate a sentence connecting percentages of groups into an algebraic relation to obtain a ratio. Given Data / Assumptions: B = number of boys; G = number of girls. 10% of boys = one-fourth of girls ⇒ 0.10B = 0.25G. Concept / Approach: Rearrange to B/G by isolating terms. Step-by-Step Solution: 0.10B = 0.25G.B/G = 0.25 / 0.10 = 2.5.Express as a ratio: 2.5 : 1 = 5 : 2. Verification / Alternative check: Pick numbers matching 5 : 2, e.g., B = 50, G = 20. Then 10% of boys = 5; one-fourth of girls = 5. Condition satisfied. Why Other Options Are Wrong: 3 : 2, 2 : 1, 4 : 3, 5 : 3 do not satisfy 0.10B = 0.25G. Common Pitfalls: Inverting the ratio (2 : 5) or mixing percent with fraction improperly. Final Answer: 5 : 2

Question 18

Successive percent change net effect: Suman’s income is first increased by 7% and then decreased by 7%. What is the net percentage change in her income?

Accepted Answer

Introduction / Context: Equal percentage increase and decrease do not cancel out, because the second change is applied on a different base. The net effect is always a small decrease equal to (a^2 / 100)% where a is the percent. Given Data / Assumptions: Increase a = 7% ⇒ factor 1.07. Then decrease 7% ⇒ factor 0.93. Concept / Approach: Net factor = 1.07 * 0.93 = 0.9951. Net % change = (0.9951 − 1) * 100%. Step-by-Step Solution: Net factor = 1 − (a^2/10000) for equal up and down changes.a = 7 ⇒ a^2 = 49 ⇒ reduction = 49/10000 = 0.0049.Net change = −0.49%. Verification / Alternative check: Start with 100. After +7% → 107. After −7% → 107 * 0.93 = 99.51. Difference from 100 = −0.49%, confirming the formula. Why Other Options Are Wrong: Options claiming increase are incorrect; the net is always a decrease. 0.39% miscomputes a^2/100. “No change” holds only for +x% and then −x% when x = 0. Common Pitfalls: Assuming +7% and −7% cancel; they do not because the bases differ. Final Answer: 0.49% (decrease)

Question 19

Percentage relation between two numbers: 48% of the first number equals 60% of the second number. Determine the ratio of the first number to the second number, keeping percentages and comparative meaning exactly as stated.

Accepted Answer

Introduction / Context: This problem tests translation of percentage statements into algebra and then simplifying to a ratio. When one percentage of a quantity equals another percentage of a different quantity, setting up an equation and simplifying is the most reliable method. Given Data / Assumptions: Let the first number be A. Let the second number be B. Statement: 48% of A equals 60% of B. We assume A and B are positive real numbers (typical in ratio questions). Concept / Approach: Convert each percentage to a decimal multiplier. Then form an equation 0.48A = 0.60B and isolate A/B (or B/A). Ratios are scale-free, so any common factors can be canceled cleanly without needing actual values of A or B. Step-by-Step Solution: 0.48A = 0.60BA/B = 0.60/0.48A/B = 60/48 = 5/4Therefore, the ratio first : second = 5 : 4. Verification / Alternative check: Pick B = 4 ⇒ A = 5. Check 48% of 5 = 2.4, 60% of 4 = 2.4, which match exactly. Hence the ratio is correct. Why Other Options Are Wrong: 4 : 7 and 3 : 4: Do not satisfy 0.48A = 0.60B upon substitution. Could not be determined: The equation uniquely determines the ratio; no ambiguity exists. Common Pitfalls: Swapping the percentages or inverting the ratio. A common error is writing 48/60 instead of 60/48 for A/B. Always solve the equation carefully. Final Answer: 5 : 4

Question 20

Percent-of-a-number equation: The sum of 15% of a positive number and 20% of the same number equals 126. What is one-third of that number?

Accepted Answer

Introduction / Context: This question assesses comfort with combining multiple percentages of the same unknown and then extracting a specific fraction (one-third) of the number. It is a straightforward linear equation involving percentages. Given Data / Assumptions: Unknown positive number = N. 15% of N plus 20% of N totals 126. We need one-third of N. Concept / Approach: Combine the percentages first: 15% + 20% = 35% of N. Convert 35% to decimal 0.35 and solve 0.35N = 126. Once N is found, compute N/3 directly. Step-by-Step Solution: 0.15N + 0.20N = 1260.35N = 126N = 126 / 0.35 = 126 * (100/35) = 126 * (20/7) = 18 * 20 = 360One-third of N = 360 / 3 = 120 Verification / Alternative check: Compute 15% and 20% of 360: 0.15*360 = 54, 0.20*360 = 72, sum = 126. The computation is consistent, so one-third is 120. Why Other Options Are Wrong: 360: That is the full N, not one-third. 1080: Triple of N; misreading the request. 40: One-ninth of N; incorrect fraction. Common Pitfalls: Adding percentages incorrectly (e.g., 15 + 20 = 30), or forgetting to divide by 3 at the end. Carefully track what is being asked: one-third of the number after finding N. Final Answer: 120

Percentage Questions