Percentages, profit and loss, discount, simple and compound interest: previous-year questions
45 real UPSC Prelims questions (2011–2026) with the official answer and a clear explanation. 12 of them came in the last five papers.
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A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?
Answer (b) & explanation
His saving rises by 30% (b). Step 1: take salary = 100. He saves 10%, so saving = 10 and expenditure = 90. Step 2: new salary = 112 (12% more). New expenditure = 99 (10% more than 90). Step 3: new saving = 112 − 99 = 13. Saving goes from 10 to 13, a rise of 3 on 10 = 30%. Options (a), (c) and (d) fail.
Tip: take 100 for the salary and split it into saving and spending. Small percentage changes in big amounts can cause large changes in the small leftover.
the saving is a small base. A 2% gap between the two growth rates becomes a 30% change in saving.
Answer as per the official UPSC answer key.
A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹ 5. At the end of the day, he also gets ₹ 2 for every kilometre of the distance covered in the day. The boy wants to earn more than ₹ 500 a day, but does not want to travel more than 100 km. Which of the following numbers of deliveries would definitely meet his target?
Answer (d) & explanation
The question cannot be answered due to insufficient data (d). Step 1: earnings = 5 × deliveries + 2 × km, and km can be anything from 0 to 100. Step 2: with 90 deliveries, he earns 450 + 2k. That crosses ₹500 only if he rides more than 25 km. With 80 or 85 deliveries he needs even more km. Step 3: we are not told how far he travels. So no option is definitely enough. Options (a), (b) and (c) would work only with enough kilometres.
Tip: "definitely" means it must work in the worst case. Here the worst case is very few kilometres, and then 101 or more deliveries would be needed.
the word "definitely" decides it. "Possibly" would give a different answer.
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Answer as per the official UPSC answer key.
The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹ 90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?
Answer (b) & explanation
He must cut his travel by 200 km (b). Step 1: to keep spending the same, price × litres must stay fixed. The price rises by 10%, from ₹90 to ₹99, so the litres he buys must fall to 100/110 = 10/11 of before. Step 2: his travel falls in the same ratio: 2200 × 10/11 = 2000 km. Step 3: so he must reduce by 2200 − 2000 = 200 km. The mileage (16 km/l) is not needed. Option (c), 220 km, wrongly takes 10% of 2200.
Tip: a 10% price rise needs a cut of 10/110 = 1/11 (about 9.1%) in use, not 10%, to keep spending the same.
a 10% rise needs a 1/11 cut (about 9.1%), not a 10% cut of 220 km.
Answer as per the official UPSC answer key.
The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?
Answer (a) & explanation
1. Put k = 0. Then the price never changes, so q = p. Check each option: (a) gives p × 10⁸ = q × 10⁸, so p = q. Works. (c) also gives p = q. (b) and (d) fail.
2. To choose between (a) and (c): each "up k%, then down k%" round multiplies the price by (10⁴ − k²) ÷ 10⁴. Example: up 10% and down 10% turns 100 into 99, and (10000 − 100) ÷ 10000 = 0·99.
3. There are two such rounds, so the bracket comes twice (squared) and 10⁴ comes twice (10⁸).
4. Answer: (a).
Answer as per the official UPSC answer key.
P’s salary is 20% lower than Q’s salary which is 20% lower than R’s salary. By how much percent is R’s salary more than P’s salary?
Answer (b) & explanation
R's salary is 56.25% more than P's (b). Step 1: let R = 100. Q is 20% lower: 80. P is 20% lower than Q: 80 − 16 = 64. Step 2: R is more than P by 100 − 64 = 36. Step 3: "more than P" means the base is P: 36/64 × 100 = 56.25%. Option (a) and the others use the wrong base or add the two 20% cuts as 40%. Two 20% cuts do not make 40%.
Tip: "X is how much more than Y" always divides by Y. Taking 100 for the top value makes chained percentages easy. Two successive cuts of 20% give a total cut of 36%, not 40%.
"more than P's salary" means divide by P, not by R.
Answer as per the official UPSC answer key.
A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?
Answer (d) & explanation
The result changes by 93.75% (d). Step 1: take an easy number, 4. The correct result is 4 × 4 = 16. The wrong result is 4 ÷ 4 = 1. Step 2: the change is 16 − 1 = 15. Step 3: as a percentage of the correct result: 15/16 × 100 = 93.75% (a fall). In general: correct = 4x, wrong = x/4, so the change is (4x − x/4)/4x = 15/16, whatever x is. Options (a), (b) and (c) are wrong.
Tip: percentage change is always measured on the correct (original) value. Picking a friendly number such as the divisor itself makes the arithmetic quick.
Answer as per the official UPSC answer key.
In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?
Answer (b) & explanation
20% failed in only one subject (b). Step 1: 15% failed both, so 85% passed in at least one subject. Step 2: passed both = 80 + 70 − 85 = 65% (adding English and Hindi counts the "both" group twice). Step 3: everyone is in one of three groups: passed both (65%), failed both (15%) or failed exactly one. So failed only one = 100 − 65 − 15 = 20%. Check: passed only English = 15%, only Hindi = 5%; total 20%. Options (a), (c) and (d) fail.
Tip: for two-subject pass/fail questions use: at least one = A + B − both. Draw two circles if you get confused.
Answer as per the official UPSC answer key.
A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?
Answer (d) & explanation
P costs ₹1,350 (d). Step 1: start with the smallest item. Let Q = 100. R is 20% more: 120. P is 25% more than R: 120 + 30 = 150. Total = 370 parts. Step 2: 370 parts = ₹3,330, so one part = ₹9. Step 3: P = 150 × 9 = ₹1,350 (R = ₹1,080, Q = ₹900; total ₹3,330). Options (a), (b) and (c) do not fit the total.
Tip: take 100 for the item everything else is based on. Then convert parts to rupees in one step. Check with the total.
Answer as per the official UPSC answer key.
A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct ?
Answer (c) & explanation
R is less than S (c). Step 1: at the same rate, half-yearly compounding gives more than annual compounding, because interest earns interest sooner. Step 2: here both give the same amount Q. So the half-yearly rate R must be smaller. Step 3: exactly: (1 + R/200)² = 1 + S/100, which gives S = R + R²/400. So S is always more than R for any positive rate. Option (a) and (d) allow equality, which is impossible. Option (b) reverses it.
Tip: more frequent compounding needs a lower rate to reach the same amount. This is why banks quote both a nominal and an effective rate.
Answer as per the official UPSC answer key.
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
Answer (b) & explanation
The resultant increase is 10% (b). Step 1: start with a price of ₹ 100. A 25% rise makes it ₹ 125. Step 2: a 20% cut on 125 is ₹ 25, bringing it to ₹ 100. Step 3: a 10% rise on 100 makes it ₹ 110. From ₹ 100 to ₹ 110 is a rise of 10%. Option (d), 15%, wrongly adds 25 − 20 + 10. Options (a) and (c) are other miscalculations.
Tip: multiply the factors: 1.25 × 0.8 × 1.1 = 1.1. A 25% rise followed by a 20% cut always cancels out exactly.
(d) 15% just adds 25 − 20 + 10. Each change works on the new price.
Answer as per the official UPSC answer key.
When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct?
Answer (a) & explanation
The order is z < x < y (a). Step 1: 70% of x + y = 165% of y. So 70% of x = 65% of y. A bigger share of x equals a smaller share of y, so y is bigger than x. Step 2: 60% of x + z = 165% of z. So 60% of x = 65% of z. A bigger share of z equals a smaller share of x, so z is smaller than x. Step 3: together: z < x < y. Options (b), (c) and (d) get the order wrong.
Tip: if a% of P = b% of Q and a is larger than b, then P is smaller than Q. The number taking the bigger percentage is the smaller one.
Answer as per the official UPSC answer key.
Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?
Answer (a) & explanation
The voters list has 15000 names (a). Step 1: there are only two candidates and no invalid votes. X got 56%, so Y got 44%. Step 2: X won by 56 − 44 = 12% of votes cast = 1440. So votes cast = 1440 ÷ 0.12 = 12000. Step 3: votes cast are 80% of the list. So the list = 12000 ÷ 0.8 = 15000. Option (b), 12000, is the votes cast, not the list. Options (c) and (d) are miscalculations.
Tip: the winning margin is the difference in percentages. Then work back step by step to the base you need.
12000 is the votes cast, not the voters list. It is the trap option.
Answer as per the official UPSC answer key.
P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score ?
Answer (a) & explanation
Q scored 360 (a). Step 1: Q scored 10% less than P. So the gap between them is 10% of P's marks. Step 2: the gap is 40 marks. So 10% of P = 40, which gives P = 400. Step 3: Q = 400 − 40 = 360. Option (c), 400, is P's score, not Q's. Options (b) 380 and (d) 420 come from using Q as the base of the percentage.
Tip: always ask "10% of whom?". Here "less than P" means P is the base. Check: 10% of 400 is 40, and 400 − 40 = 360.
10% less than P, so the base is P, not Q.
Answer as per the official UPSC answer key.
If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price ?
Answer (a) & explanation
There is no net change, 0% (a). Step 1: a 20% cut means multiplying by 0.8. Step 2: a 25% rise on the new price means multiplying by 1.25. Step 3: 0.8 × 1.25 = 1. So the final price equals the starting price. Options (b) and (c) wrongly add or subtract the percentages (25 − 20 = 5). Option (d) is wrong because the multipliers settle it without knowing the price.
Tip: for successive percentage changes, multiply the factors. A shortcut is a + b + ab/100: −20 + 25 − 500/100 = 0.
don't just add –20 and +25. The 25% is taken on the reduced price.
Answer as per the official UPSC answer key.
A biology class at high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population ?
Answer (d) & explanation
The model is P = 50(2)^(n/12) (d). Step 1: doubling means multiplying, not adding. So the linear options (a) and (b) are out. Step 2: after 12 years, there should be exactly one doubling. Put n = 12: 2^(12/12) = 2¹ = 2, so P = 100. Correct. Step 3: option (c), 2^(12n), at n = 12 gives 2¹⁴⁴, which is absurdly large. So only (d) fits. After 24 years, (d) gives 50 × 4 = 200, again correct.
Tip: for growth that doubles every T years, use P = P₀ × 2^(n/T). Test an easy value of n to check any formula quickly.
Answer as per the official UPSC answer key.
In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys ?
Answer (d) & explanation
20% of foreign students are boys (d). Step 1: take 100 students. 60 are Indian, and 30% of them, 18, are girls. Step 2: total girls = 50, so foreign girls = 50 − 18 = 32. Foreign students = 100 − 60 = 40. So foreign boys = 40 − 32 = 8. Step 3: the question asks for a share of foreign students: 8 ÷ 40 = 20%. Option (a), 45%, and the others fail. Note 8% of the whole class is also a trap if you forget to divide by 40.
Tip: always check the base of the percentage. "Percentage of foreign students" means divide by the foreign total, not the class total.
"30% of the Indian students" is not 30% of the whole class.
Answer as per the official UPSC answer key.
A person bought a car and sold it for ₹ 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?
Answer (d) & explanation
He spent ₹ 3,75,000 on the car (d). Step 1: a 20% loss means he got back 80% of what he paid. Step 2: 80% = ₹ 3,00,000, so 1% = 3,00,000 ÷ 80 = ₹ 3,750. Step 3: 100% = ₹ 3,75,000. Check: 20% of 3,75,000 is 75,000, and 3,75,000 − 75,000 = 3,00,000. Option (a), ₹ 3,60,000, wrongly adds 20% of the selling price. Options (b) and (c) fail.
Tip: loss and profit % are always on the cost price. So cost = selling price ÷ (1 − loss%). Adding 20% to the selling price is the classic trap.
(a) adds 20% to 3,00,000. The 20% is of the buying price, not the selling price.
Answer as per the official UPSC answer key.
A shop owner offers the following discount options on an article to a customer :
- 1. Successive discounts of 10% and 20%, and then pay a service tax of 10%
- 2. Successive discounts of 20% and 10%, and then pay a service tax of 10%
- 3. Pay a service tax of 10% first, then successive discounts of 20% and 10%
Which one of the following is correct?
Answer (d) & explanation
All three options are equally good (d). Step 1: each option multiplies the price by the same three numbers: 0·9 (10% off), 0·8 (20% off) and 1·1 (10% tax). Step 2: multiplication can be done in any order: 0·9 × 0·8 × 1·1 = 0·8 × 0·9 × 1·1 = 1·1 × 0·8 × 0·9 = 0·792. Step 3: so the final price is the same in all three. Options (a), (b) and (c) fail.
Tip: successive percentage changes multiply, so their order never matters. Two successive discounts of 20% and 10% equal a single 28% discount, not 30%.
Answer as per the official UPSC answer key.
In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?
Answer (c) & explanation
34 2/7% of adults are married (c). Step 1: each married man has one wife, so married men = married women. So 0·4M = 0·3W, which gives M : W = 3 : 4. Step 2: take M = 300 and W = 400. Married men = 40% of 300 = 120; married women = 30% of 400 = 120. Total married = 240 out of 700. Step 3: 240 ÷ 700 = 24/70 = 34 2/7%. Option (d), 35%, simply averages 40 and 30. Options (a) and (b) fail.
Tip: never average percentages of groups of different sizes. Find the group ratio first, then use real numbers.
Answer as per the official UPSC answer key.
As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for ₹ 1,200. What was the original price of rice per kg?
Answer (b) & explanation
The original price was ₹ 40 per kg (b). Step 1: a 25% price rise means the same money buys 4/5 as much. So quantity falls by 1/5. Step 2: that 1/5 equals 6 kg. So the old quantity = 6 × 5 = 30 kg. Step 3: old price = 1200 ÷ 30 = ₹ 40. Check: new price = ₹ 50; 1200 ÷ 50 = 24 kg, which is 6 kg less. Options (a), (c) and (d) fail this check.
Tip: price up by 1/4 means quantity down by 1/5 (for fixed spending). Price up by 1/n means quantity down by 1/(n + 1).
Answer as per the official UPSC answer key.