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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Questions per year, counted from the official papers.
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As per agreement with a bank, a businessman had to refund a loan in some equal instalments without interest. After paying 18 instalments he found that 60 percent of his loan was refunded. How many instalments were there in the agreement?
Answer (c) & explanation
There were 30 instalments (c). Step 1: 18 instalments cleared 60% of the loan. The instalments are equal and there is no interest, so every instalment clears the same share. Step 2: each instalment clears 60 ÷ 18 = 3⅓%. Step 3: to clear 100%, he needs 100 ÷ 3⅓ = 30 instalments. A faster way: 18 is 60%, so 100% is 18 ÷ 0.6 = 30. Options (a), (b) and (d) do not give 100%.
Tip: this is simple proportion. If 60% takes 18, then 10% takes 3, and 100% takes 30. Breaking it into 10% chunks makes the maths easy without a calculator.
Answer as per the official UPSC answer key.
Out of 120 applications for a post, 70 are male and 80 have a driver's license. What is the ratio between the minimum to maximum number of males having driver's license?
Answer (c) & explanation
3 to 7 is correct (c). Step 1: the maximum number of licensed males is when all 70 males have a licence: 70 (there are 80 licences, enough). Step 2: the minimum is when overlap is as small as possible: 70 males + 80 licence-holders = 150, but there are only 120 people, so at least 150 − 120 = 30 must be both. Step 3: minimum : maximum = 30 : 70 = 3 : 7. So (a), (b) and (d) fail.
Tip: for two groups in a fixed total, maximum overlap = the smaller group; minimum overlap = sum of groups − total (or zero if that is negative). Draw two circles inside a box to see it.
Answer as per the official UPSC answer key.
The tank-full petrol in Arun's motorcycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full petrol last?
Answer (d) & explanation
8 days is correct (d). Step 1: let the tank hold 10 units, so he uses 1 unit a day for 10 days. Step 2: using 25% more means 1.25 units a day. Step 3: days = 10 ÷ 1.25 = 8. So (a), (b) and (c) fail.
Tip: when use per day goes up by 25%, the days do not fall by 25% (which would give 7.5). They fall to 1 ÷ 1.25 = 4/5 of the old figure, a 20% drop. Remember: a 25% rise is undone by a 20% fall. This pair (25% up, 20% down) appears often in CSAT, so it is worth memorising, along with 50% up and 33⅓% down.
Answer as per the official UPSC answer key.
There are 100 students in a particular class. 60% students play cricket, 30% students play football and 10% students play both the games. What is the number of students who play neither cricket nor football?
Answer (b) & explanation
20 students is correct (b). Step 1: 60 play cricket and 30 play football. But the 10 who play both are counted twice. Step 2: students playing at least one game = 60 + 30 − 10 = 80. Step 3: students playing neither = 100 − 80 = 20. So (a), (c) and (d) fail.
Tip: for two overlapping groups, total in either = A + B − both. Drawing two overlapping circles (a Venn diagram) makes this clear at a glance.
Answer as per the official UPSC answer key.
In a group of persons, 70% of the persons are male and 30% of the persons are married. If two-sevenths of the males are married, what fraction of the females is single?
Answer (d) & explanation
2/3 is correct (d). Step 1: take 100 people. Males = 70, females = 30. Married = 30 in total. Step 2: two-sevenths of males are married: 2/7 × 70 = 20 married males. So married females = 30 − 20 = 10. Step 3: single females = 30 − 10 = 20. The fraction of females who are single = 20 ÷ 30 = 2/3. So (a), (b) and (c) fail.
Tip: for percentage puzzles, assume a total of 100. It turns every percentage into a simple number you can add and subtract.
the fraction is of the females, not of the whole group.
Answer as per the official UPSC answer key.