Question 1

A salary increases from ₹ 7200 to ₹ 8100. By what percentage has the salary increased?

Accepted Answer

Introduction / Context: Percentage change problems require computing the change relative to the original value. Here, the original salary and the new salary are given directly. Given Data / Assumptions: Original salary = ₹ 7200. New salary = ₹ 8100. Concept / Approach: Percentage increase = (Increase / Original) * 100. Increase equals New − Original. Always divide by the original amount when computing the rate of increase. Step-by-Step Solution: Increase = 8100 − 7200 = 900Rate = (900 / 7200) * 100 = 0.125 * 100 = 12.5%12.5% = 12 1/2% Verification / Alternative check: Compute 12.5% of 7200: 0.125 * 7200 = 900. Add to 7200 to get 8100, confirming the result. Why Other Options Are Wrong: 25%, 18%, 16 2/3%, and 15% correspond to different increases; none produce exactly ₹ 8100 from ₹ 7200. Common Pitfalls: Dividing by the new amount instead of the original, which would understate the true percentage change. Final Answer: 12 1/2%

Question 2

If A’s income is 5/6 of B’s income, by what percent is B’s income more than A’s income?

Accepted Answer

Introduction / Context: Problems comparing two quantities often ask “how much percent more/less.” The base for the percentage must be the quantity named after “than”. Here, B is compared to A, so A is the base. Given Data / Assumptions: A = (5/6) * B. Find ((B − A)/A) * 100. Concept / Approach: From A = (5/6)B, divide both sides by A to express B in terms of A, or directly compute (B − A)/A. This yields the percentage by which B exceeds A. Step-by-Step Solution: A = (5/6)B ⇒ B − A = B − (5/6)B = (1/6)B(B − A)/A = [(1/6)B] / [(5/6)B] = 1/5Percentage = (1/5) * 100 = 20% Verification / Alternative check: Let B = 60. Then A = 50. B is 10 more than A; 10/50 = 20%—consistent. Why Other Options Are Wrong: 12 1/2%, 15%, 16 2/3%, 25% stem from choosing the wrong base or arithmetic slips. Common Pitfalls: Using B as the base (computing (B − A)/B), which answers a different question and gives 16 2/3% instead of the requested 20%. Final Answer: 20%

Question 3

25% of what amount equals 12 1/2% of ₹ 180? Find the amount.

Accepted Answer

Introduction / Context: Here we equate two percentages of different bases. Converting the verbal statement into an equation allows solving for the unknown base amount directly. Given Data / Assumptions: x is the unknown amount. 25% of x = 12.5% of 180. Percentages are standard base-100 rates. Concept / Approach: Write 25% as 0.25 and 12.5% as 0.125. Set 0.25x = 0.125 * 180 and solve for x. Using fractions (1/4 and 1/8) is another quick method. Step-by-Step Solution: 0.25x = 0.125 * 1800.125 * 180 = 22.50.25x = 22.5 ⇒ x = 22.5 / 0.25 = 90 Verification / Alternative check: Compute both sides at x = 90: 25% of 90 = 22.5; 12.5% of 180 = 22.5. Equality holds. Why Other Options Are Wrong: ₹ 80 and ₹ 75 give too small a 25%; ₹ 120 gives 30, which is too large; ₹ 100 gives 25, not 22.5. Common Pitfalls: Interpreting “12 1/2 of ₹ 180” without the percent; in standard aptitude, it denotes 12.5% unless otherwise stated. Final Answer: ₹ 90

Question 4

30% of a three-digit number is 190.8. What is 125% of that number?

Accepted Answer

Introduction / Context: We are given a partial percentage of a number and asked to compute a larger percentage of the same number. This is a straightforward two-step percentage scaling task. Given Data / Assumptions: 0.30 * N = 190.8. Need 1.25 * N. N is a three-digit positive number. Concept / Approach: First recover N by dividing the known part by its percentage. Then scale N by 125% (which equals 1.25 * N). Using proportionality avoids unnecessary rounding. Step-by-Step Solution: N = 190.8 / 0.30 = 636125% of N = 1.25 * 636 = 795 Verification / Alternative check: Compute 30% of 636 to reconfirm: 0.30 * 636 = 190.8. The number is consistent; 1.25 * 636 = 795 as found. Why Other Options Are Wrong: Values like 759, 785, 779, 765 result from arithmetic slips (e.g., using 1.2 instead of 1.25 or miscomputing the base N). Common Pitfalls: Dividing by 30 instead of 0.30; remember percentages translate to decimals for multiplication and division. Final Answer: 795

Question 5

A person’s monthly income is ₹ 5000 and increases by 30%. What is the new monthly income?

Accepted Answer

Introduction / Context: This is a simple percentage increase problem, illustrating direct scaling of a base value by a given rate. Such questions are common in salary and price adjustments. Given Data / Assumptions: Original monthly income = ₹ 5000. Increase = 30% of original. Concept / Approach: New income = Original * (1 + rate). For a 30% increase, multiply by 1.30. Ensure the base is the original amount, not the increment. Step-by-Step Solution: Increase = 0.30 * 5000 = 1500New income = 5000 + 1500 = 6500 Verification / Alternative check: Direct scaling: 5000 * 1.30 = 6500. Same result. Why Other Options Are Wrong: ₹ 7000 implies a 40% increase; ₹ 5500 implies 10%; ₹ 4500 is a decrease; ₹ 6000 is 20% increase, not 30%. Common Pitfalls: Adding 30 to 5000 (confusing percent with absolute units). Always convert the percent to a proportion of the base. Final Answer: ₹ 6500

Question 6

When 35 is subtracted from a number it becomes 80% of itself. What is 4/5 of that original number?

Accepted Answer

Introduction / Context: This is a linear equation framed via a percentage condition. The phrase “it reduced to 80%” means the new value equals 0.8 times the original number. Solve for the original, then compute 4/5 of it. Given Data / Assumptions: N − 35 = 0.8N. Need 4/5 of N. Concept / Approach: Rearrange the equation to isolate N. After finding N, multiply by 4/5 (or 0.8) to obtain the requested fraction of the original. Step-by-Step Solution: N − 35 = 0.8N ⇒ N − 0.8N = 350.2N = 35 ⇒ N = 35 / 0.2 = 1754/5 of N = 0.8 * 175 = 140 Verification / Alternative check: Check the condition: 175 − 35 = 140; 80% of 175 is also 140. Consistent. Why Other Options Are Wrong: 70, 90, 120, 160 correspond to applying 4/5 to the wrong number or mis-solving the equation for N. Common Pitfalls: Treating 80% as subtracting 80 (absolute) rather than 0.8N (relative). Always use proportional change for percentages. Final Answer: 140

Question 7

If Vandana’s income is 25% more than Aarti’s income, then Aarti’s income is how much percent less than Vandana’s?

Accepted Answer

Introduction / Context: “More than” and “less than” percentages are not symmetric. If V is 25% more than A, then A is not 25% less than V. This item checks understanding of the reverse percentage relationship. Given Data / Assumptions: V = 1.25A. Find (V − A)/V * 100. Concept / Approach: Compute A’s shortfall relative to V using V as the base (because the phrase asks “less than Vandana’s”). Then convert the fraction to a percentage. Step-by-Step Solution: Difference = V − A = 1.25A − A = 0.25ARelative to V: (V − A)/V = 0.25A / (1.25A) = 0.2Percentage = 0.2 * 100 = 20% Verification / Alternative check: Example: let A = 100; V = 125. A is 25 less than 125, which is 25/125 = 20% less. Why Other Options Are Wrong: 25% confuses symmetric change; 18%, 21%, 24% are arithmetic distractors not matching the ratio 100:125. Common Pitfalls: Using A as base by mistake, which answers a different question and yields 25%—not what was asked. Final Answer: 20%

Question 8

Basic percent of a whole: 50 kg is what percent of 250 kg?

Accepted Answer

Introduction / Context: This is a direct percent-of-whole computation: part divided by whole, then converted to a percentage. Units cancel as both quantities are in kilograms. Given Data / Assumptions: Part = 50 kg. Whole = 250 kg. Concept / Approach: Percentage = (Part / Whole) * 100. Ensure the base (whole) is the 250 kg amount, not the 50 kg amount. Step-by-Step Solution: (50 / 250) * 100 = 0.2 * 100 = 20% Verification / Alternative check: Since 50 is one-fifth of 250, the percent is 20% (because 1/5 = 20%). Why Other Options Are Wrong: 15%, 18%, 25%, 26% do not reflect the 1:5 ratio. Common Pitfalls: Accidentally dividing 250 by 50 (giving 500%) or forgetting to multiply by 100. Final Answer: 20%

Question 9

Compute 32% of (3/8) of 5000. What is the value?

Accepted Answer

Introduction / Context: Nested percentage and fraction problems are best handled stepwise. First take the fractional part, then the percentage of the result (or multiply the factors together first, if convenient). Given Data / Assumptions: Total = 5000. Fraction = 3/8. Percentage = 32% = 0.32. Concept / Approach: Either compute 5000 * (3/8) = 1875, then take 32% of 1875, or multiply factors: 5000 * 3/8 * 0.32. Both methods yield the same exact result. Step-by-Step Solution: (3/8) of 5000 = 5000 * 3/8 = 187532% of 1875 = 0.32 * 1875 = 600 Verification / Alternative check: Combined factor: 3/8 = 0.375; 0.375 * 0.32 = 0.12; 0.12 * 5000 = 600. Same result. Why Other Options Are Wrong: 606, 610, 580, 640 are near misses from rounding or arithmetic slips; the exact arithmetic gives 600. Common Pitfalls: Using 0.28 instead of 0.32, or taking 32% of 5000 first and then 3/8 incorrectly. Order does not matter if multiplication is exact, but inputs must be correct. Final Answer: 600

Question 10

A rectangle’s length becomes half and its breadth becomes double. The resultant area is what percent of the original area?

Accepted Answer

Introduction / Context: This problem examines how proportional changes in dimensions affect area. For rectangles, area equals length * breadth, so scaling factors multiply directly to give the new area factor. Given Data / Assumptions: Original area A = L * B. New length L′ = (1/2) * L. New breadth B′ = 2 * B. Concept / Approach: The new area A′ equals L′ * B′. Substitute the scaled dimensions and compute the ratio A′/A. Convert that ratio to a percentage of the original area. Step-by-Step Solution: A′ = L′ * B′ = (1/2)L * (2B) = (1/2 * 2) * L * BA′ = 1 * L * B = ATherefore, A′/A = 1 ⇒ A′ is 100% of A Verification / Alternative check: Choose numbers: L = 10, B = 5 ⇒ A = 50. New: L′ = 5, B′ = 10 ⇒ A′ = 50. Same area confirms 100%. Why Other Options Are Wrong: 75%, 80%, 55%, 25% would imply net shrinking; however, the halving and doubling exactly cancel out, leaving the area unchanged. Common Pitfalls: Adding percent changes (−50% + 100% = 50%) is incorrect because area depends on the product, not a sum. Always multiply the scale factors. Final Answer: 100%

Question 11

Two numbers are 20% and 50% more than a third number. The second is what percent of the first?

Accepted Answer

Introduction / Context: This compares two quantities each defined relative to a common third quantity. Using a convenient base for the third number simplifies percentage comparisons. Given Data / Assumptions: Let the third number be T. First number F = T * 1.20. Second number S = T * 1.50. Find S as a percent of F: (S/F) * 100. Concept / Approach: Because both are scaled from the same base, T cancels out in the ratio S/F. Compute (1.50 / 1.20) * 100 to get the required percentage. Step-by-Step Solution: S/F = (1.50T) / (1.20T) = 1.50 / 1.20 = 15/12 = 5/4Percentage = (5/4) * 100 = 125% Verification / Alternative check: Assume T = 100. Then F = 120, S = 150. S as percent of F = (150/120)*100 = 125%. Why Other Options Are Wrong: 90%, 80%, 75%, 120% reflect using the wrong base or arithmetic errors; the exact ratio is 5:4. Common Pitfalls: Confusing “percent more than third” with “percent of the first”. Always form the requested ratio explicitly. Final Answer: 125%

Question 12

Passing threshold and shortfall: A student must score 780 marks to pass. Sonu scored 728 and failed by 5%. What are the maximum aggregate marks?

Accepted Answer

Introduction / Context: This question connects a fixed pass mark with a stated failure margin in percentage terms of the aggregate (total) marks. The key is to interpret “failed by 5%” as a shortfall equal to 5% of the total possible marks. Given Data / Assumptions: Pass mark = 780. Sonu’s mark = 728. Shortfall to pass = 780 − 728 = 52. “Failed by 5%” ⇒ Shortfall = 5% of total aggregate. Concept / Approach: Let total marks be M. Then 5% of M equals the shortfall 52. Solve M from 0.05M = 52. This yields the required aggregate marks for the exam. Step-by-Step Solution: Shortfall = 780 − 728 = 52Interpretation: 52 = 5% of total ⇒ 52 = 0.05 * MM = 52 / 0.05 = 1040 Verification / Alternative check: 5% of 1040 is 52. Adding this to Sonu’s 728 gives 780, the pass mark. Thus the interpretation and arithmetic are consistent. Why Other Options Are Wrong: 1000 gives 5% = 50 (short by 2); 1100 gives 55 (too large); “Cannot be determined” is incorrect since the shortfall percentage is specified. Common Pitfalls: Misreading “failed by 5%” as 5% of 780 or 5% of Sonu’s marks; the standard usage is relative to the total possible marks. Final Answer: 1040

Question 13

Five subjects, each out of 100: Hindi 76, Science 48, Mathematics 84, Social Science 38, English 72. What is the overall percentage?

Accepted Answer

Introduction / Context: Overall percentage across subjects is computed using total marks obtained divided by total maximum marks, then multiplied by 100. Each subject carries equal maximum marks here, simplifying the computation. Given Data / Assumptions: Marks: 76, 48, 84, 38, 72. Maximum per subject = 100; number of subjects = 5. Concept / Approach: Sum the marks to get total obtained. Maximum total = 5 * 100 = 500. Overall percentage = (Total obtained / 500) * 100. Step-by-Step Solution: Total = 76 + 48 + 84 + 38 + 72 = 318Overall % = (318 / 500) * 100 = 63.6% Verification / Alternative check: Compute the average per subject: 318/5 = 63.6. Since each subject is out of 100, the average equals the overall percentage directly. Why Other Options Are Wrong: 63.8%, 62.6%, 64.8% come from addition or division slips; 62% is a rounded-down estimate, not exact. Common Pitfalls: Forgetting that each subject has equal weight; when maxima differ, a weighted calculation would be required. Final Answer: 63.6%

Question 14

A saves 20% of his monthly salary. If his monthly expenditure is ₹ 6000, what is his monthly saving?

Accepted Answer

Introduction / Context: Let total salary be S. If 20% is saved, then 80% is spent. Given the expenditure, we can find S and then the saving (20% of S). This is a standard split between savings and expenses. Given Data / Assumptions: Savings rate = 20% of salary. Expenditure = ₹ 6000 = 80% of salary. Concept / Approach: Expenditure = 0.80 * S ⇒ S = Expenditure / 0.80. Once S is known, Saving = 0.20 * S. Avoid mixing rupees with percentages directly; use decimal multipliers. Step-by-Step Solution: S = 6000 / 0.80 = 7500Saving = 0.20 * 7500 = 1500 Verification / Alternative check: Check: Saving 1500 plus expenditure 6000 equals 7500, which matches the computed salary. Why Other Options Are Wrong: ₹ 1200 and ₹ 1000 underestimate the saving; ₹ 1800 overestimates it; ₹ 4800 is actually the remaining amount after a mistaken 20% spend assumption. Common Pitfalls: Taking 20% of ₹ 6000 instead of 20% of the total salary. Expenditure is 80% of salary, not the base for savings percent. Final Answer: ₹ 1500

Question 15

A’s salary is 20% less than B’s salary. By what percent is B’s salary more than A’s salary?

Accepted Answer

Introduction / Context: This is the reverse of a “percent less than” statement. If A is 20% less than B, then B is more than A by a larger percentage than 20%, because the base has changed to A. Given Data / Assumptions: A = 0.80B. Find (B − A)/A * 100. Concept / Approach: Express the difference relative to A since the question asks “more than A’s salary”. Substitute A = 0.80B and simplify the ratio. Step-by-Step Solution: (B − A)/A = (B − 0.80B) / (0.80B) = 0.20B / 0.80B = 0.25Percentage = 0.25 * 100 = 25% Verification / Alternative check: Let B = 100; A = 80. B is 20 more than A; 20/80 = 25%—consistent. Why Other Options Are Wrong: 33 1/2% and 22 1/2% are unrelated; 16 2/3% uses B as base instead of A; 20% is the forward change, not the reverse. Common Pitfalls: Assuming the reverse percent is the same magnitude; it rarely is unless the percent is 0 or 100. Final Answer: 25%

Question 16

An article priced at ₹ 100 undergoes a 10% increase and then another 10% increase. By how much has the price increased in total (in ₹)?

Accepted Answer

Introduction / Context: Successive percentage changes compound multiplicatively. Two increases of 10% each do not simply add to 20%; the second 10% applies to the already increased amount. Given Data / Assumptions: Initial price = ₹ 100. Increase 1: +10%. Increase 2: +10% again. Concept / Approach: After one 10% increase, multiply by 1.10. Apply the second 10% increase by multiplying by 1.10 again. Subtract the original to get the total absolute increase. Step-by-Step Solution: After first increase: 100 * 1.10 = 110After second increase: 110 * 1.10 = 121Total increase = 121 − 100 = 21 Verification / Alternative check: Equivalent single multiplier = 1.10 * 1.10 = 1.21, which is a 21% increase on ₹ 100, i.e., ₹ 21. Why Other Options Are Wrong: 20 ignores compounding; 110 and 121 are prices, not increases; 19 is arbitrary. Common Pitfalls: Adding percentages linearly for successive changes; percentages compound unless specified otherwise. Final Answer: 21

Question 17

A man sells a chair and a table at ₹ 4000 each and breaks even overall. If the chair was sold at 25% profit, what was the percentage loss on the table?

Accepted Answer

Introduction / Context: The trader sells two items at the same price and neither gains nor loses overall, meaning total selling price equals total cost price. Given a profit on one item, the other must incur an offsetting loss. This is a standard paired transaction scenario. Given Data / Assumptions: SP (chair) = SP (table) = ₹ 4000. Overall: total SP = total CP. Chair sold at 25% profit. Concept / Approach: Let chair CP = x. Then 1.25x = 4000 ⇒ x = 3200. Let table CP = y. Total CP = x + y must equal total SP = 8000. Hence y = 8000 − 3200 = 4800. Table loss% = (y − SP)/y * 100. Step-by-Step Solution: Chair: 1.25x = 4000 ⇒ x = 3200Total CP = x + y = 3200 + yTotal SP = 4000 + 4000 = 8000 ⇒ 3200 + y = 8000 ⇒ y = 4800Loss on table = 4800 − 4000 = 800Loss% = 800/4800 * 100 = 16.666…% ≈ 16.66% Verification / Alternative check: Total CP = 3200 + 4800 = 8000 equals total SP = 8000, confirming no overall gain or loss. Why Other Options Are Wrong: 16% and 16.33% are approximations from rounding errors; 18.66% and 20% are too large given the needed balance. Common Pitfalls: Applying average of percentages instead of the actual cost bases; percentages must be computed on the correct cost price for each item. Final Answer: 16.66%

Question 18

Rakesh deposits 15% of his salary in a fixed deposit, then spends 30% of the remainder on groceries. If cash in hand is ₹ 2380, what is his salary?

Accepted Answer

Introduction / Context: This problem chains two percentage operations on the same base (salary). First a fixed-deposit deduction, then an expense from the remainder. The final leftover cash is given; reverse the operations to find the salary. Given Data / Assumptions: Salary = S. Fixed deposit = 15% of S ⇒ remainder = 85% of S. Groceries = 30% of remainder ⇒ groceries = 0.30 * 0.85S = 0.255S. Cash in hand = remainder − groceries = 0.85S − 0.255S = 0.595S = ₹ 2380. Concept / Approach: Translate each step to multipliers. The leftover factor after both steps is 0.595. Solve S from 0.595S = 2380. Using fraction 0.595 = 119/200 makes exact arithmetic straightforward. Step-by-Step Solution: 0.595S = 2380S = 2380 / 0.595 = 2380 * (200/119) = 476000 / 119 = 4000 Verification / Alternative check: Check forward: FD = 15% of 4000 = 600; remainder = 3400. Groceries = 30% of 3400 = 1020; cash = 3400 − 1020 = 2380. Matches given. Why Other Options Are Wrong: 35000, 45000, 5000, 4200 are inconsistent with the leftover factor 0.595; substituting them does not yield ₹ 2380 cash. Common Pitfalls: Taking 30% of the original salary instead of the remainder, or subtracting percentages additively (15% + 30% = 45%) which ignores compounding on the remainder. Final Answer: 4000

Question 19

A man donates 5% of his income to a charitable organisation and then deposits 20% of the remaining amount in a bank. If the cash still left with him after these two actions is ₹1919, what was his original income in rupees?

Accepted Answer

Introduction / Context: Percentage chain problems test your ability to apply successive percentage changes to a base value and track what remains. Here, part of the income is donated, then a further percentage of the remainder is deposited, and the leftover cash is given. We must reverse the steps to find the original income. Given Data / Assumptions: Donation = 5% of income. Deposit = 20% of what remains after the donation. Cash finally left = ₹1919. All percentages are on their stated bases, and amounts are exact. Concept / Approach: If I is the income, after donating 5%, remaining = 95% of I = 0.95I. Then 20% of that is deposited, so cash left is 80% of the remainder, i.e., 0.80 * 0.95I = 0.76I. Set 0.76I equal to the known leftover ₹1919 and solve for I. Step-by-Step Solution: Let income be I.After donation: remainder = 0.95I.After deposit: cash left = 0.80 * 0.95I = 0.76I.Given 0.76I = 1919 ⇒ I = 1919 / 0.76 = 2525. Verification / Alternative check: From ₹2525: 5% donation = ₹126.25; remainder ₹2398.75. Deposit 20% = ₹479.75; cash left = ₹2398.75 − ₹479.75 = ₹1919. Correct. Why Other Options Are Wrong: 2500 or 2300 would not reproduce ₹1919 after the two steps; 2558.60 arises from rounding mistakes when inverting 0.76. Common Pitfalls: Applying both percentages to the original income or adding percentages directly. Successive changes must be multiplicative. Final Answer: Rs. 2525

Question 20

A number is increased to 137 1/2% (i.e., to 1.375 times itself) and the result is 33. What is the original number?

Accepted Answer

Introduction / Context: Problems involving a number being changed to a certain percent are straightforward reverse-percentage tasks. “Increased to 137 1/2%” means the final value equals 137.5% of the original, not that 137.5% was added. Given Data / Assumptions: Final value = 33. Final value equals 137 1/2% of original. 137 1/2% = 137.5% = 11/8 as a multiplier. Concept / Approach: Convert the mixed percent to a multiplier. If original is x, then (11/8)*x = 33. Solve for x by dividing 33 by 11/8 (equivalently multiplying by 8/11). Step-by-Step Solution: Let x be the number.Final = (11/8)x = 33.x = 33 * (8/11) = 3 * 8 = 24. Verification / Alternative check: Increase 24 to 137.5%: 24 * 1.375 = 33. Correct. Why Other Options Are Wrong: 22, 25, and 27 do not yield 33 when multiplied by 1.375; they result from misinterpreting “increase to” as “increase by.” Common Pitfalls: Treating “to 137 1/2%” as adding 137.5% to the original (which would mean 237.5%). Always translate to a multiplier. Final Answer: 24

Percentage Questions