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 = 120Verification / 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

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