CSAT (Paper II): previous-year questions
1280 real UPSC Prelims questions (2011–2026) with the official answer and a clear explanation. 400 of them came in the last five papers.
How often UPSC asks this
Questions per year, counted from the official papers.
Subtopics
Arrangements, ranking, ordering and puzzles
142 questions
Clocks and calendars
5 questions
Coding-decoding, series, patterns, cubes, dice and visual reasoning
110 questions
Communication, interpersonal skills and decision-making
10 questions
Counting, permutations, combinations and probability
1 questions
Directions, blood relations and Venn diagrams
60 questions
General English: grammar, vocabulary and comprehension
20 questions
General Hindi: grammar, vocabulary, dialects and comprehension
25 questions
Geometry and mensuration
26 questions
Number system and basic algebra (divisibility, HCF/LCM, remainders, digits, equations)
196 questions
Percentages, profit and loss, discount, simple and compound interest
47 questions
Ratio, proportion, averages, mixtures and alligation
47 questions
Syllogisms, statements and conclusions, assumptions and arguments
89 questions
Time and work; pipes and cisterns
2 questions
Time, speed and distance; trains, boats and streams; races
48 questions
Attempt the questions
Newest papers first. Tap an option; the answer and the reason appear instantly.
What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?
Answer (a) & explanation
Water equal to 20% of the honey must be added (a). Step 1: take 100 litres of honey costing ₹1 a litre, so ₹100 in all. Step 2: a 20% gain means selling for ₹120. Since the mixture is sold at the honey price of ₹1 a litre, we need 120 litres of mixture. Step 3: water added = 120 − 100 = 20 litres, which is 20% of the honey. Options (b), (c) and (d) are too small. (Water is free, so all the extra volume is profit.)
Tip: in "sell at cost price and still gain" questions, the gain comes entirely from the free item. Gain% = water added as a % of the original liquid.
read the base: UPSC asks for water as a percent of honey, not of the mixture.
Answer as per the official UPSC answer key.
If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?
Answer (a) & explanation
A must be 9 (a). Step 1: AB + CD = 1CE. Two two-digit numbers add to at most 198, so the hundreds digit 1 comes from a carry. Step 2: in the tens column, A + C + (carry from units) gives a result ending in C, with a carry of 1. So A + carry = 10. Step 3: A is a single digit, so the carry from units must be 1 and A = 9. (Example: 97 + 25 = 122 fails distinctness, but 98 + 27 = 125 works: A = 9, C = 2, E = 5.) Option (d) is wrong, since A is fixed.
Tip: in letter-sum puzzles, start with the carries. A sum of two two-digit numbers can carry only 1 into the hundreds.
Answer as per the official UPSC answer key.
In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q − S = 2S and T = R + S + 3, then what is the value of P + R − T?
Answer (b) & explanation
1. Q − S = 2S means Q = 3S. From the list, (S, Q) is (4, 12) or (5, 15).
2. If S = 4, Q = 12: T = R + 7 must come from 5, 10, 15. No pair works. So S = 5, Q = 15.
3. Then T = R + 8 from 4, 10, 12: R = 4, T = 12, and P = 10. P + R − T = 10 + 4 − 12 = 2.
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.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : What are the values of m and n, where m and n are natural numbers?
Statement-I : m + n > mn and m > n.
Statement-II : The product of m and n is 24.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (c) & explanation
Both statements together are needed (c). Step 1: statement I: m + n > mn can be rewritten as (m − 1)(n − 1) < 1. With natural numbers, this means one of them is 1. Since m > n, n = 1, but m could be anything. Not enough. Step 2: statement II: mn = 24 allows 1 × 24, 2 × 12, 3 × 8 and 4 × 6. Not enough. Step 3: together: n = 1, so m = 24. A single answer. Options (a), (b) and (d) fail.
Tip: rearrange inequalities into a product form like (m − 1)(n − 1). It quickly shows which values are possible.
Answer as per the official UPSC answer key.
In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, −, × each at most two times. What is the smallest non-negative value of the expression?
Answer (d) & explanation
The smallest non-negative value is 0 (d). Step 1: zero is the smallest non-negative number, so first check whether 0 is possible. Step 2: try 5 − 4 − 3 + 2 × 1. Multiplication comes first (BODMAS): 2 × 1 = 2. Step 3: then 5 − 4 − 3 + 2 = 0. We used minus twice, plus once and times once, which the rule ("each at most two times") allows. Since 0 is reachable, options (a) 3, (b) 2 and (c) 1 cannot be the smallest.
Tip: when asked for the smallest or largest value, test the extreme option first. If it works, you are done. Always remember that × and ÷ are done before + and −.
always test the extreme option first. If 0 works, nothing smaller can be the answer.
Answer as per the official UPSC answer key.
The calendar for the year 2025 is same for
Answer (c) & explanation
2031 has the same calendar as 2025 (c). Step 1: an ordinary year moves the weekday forward by 1 day; a leap year by 2. Step 2: add the shifts from 2025: 2025 (1) + 2026 (1) + 2027 (1) + 2028 (2, leap) + 2029 (1) + 2030 (1) = 7, which is 0 extra days. So 2031 starts on the same weekday as 2025. Step 3: 2031 is also not a leap year, like 2025, so the whole calendar matches. Options (a) 2029, (b) 2030 and (d) 2033 do not add up to a multiple of 7.
Tip: keep adding odd days until you reach a multiple of 7, and check that both years are the same type (leap or ordinary).
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
P, Q, R and S appeared in a test.
Question : Has P scored more marks than Q?
Statement-I : The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.
Statement-II : The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
1. Test with numbers that obey both statements.
2. P = 1, Q = 3, R = 0, S = 4. Statement I: 1 + 3 = 0 + 4. Statement II: 1 + 4 = 5 is more than 3 + 0 = 3. Both hold, and P is less than Q.
3. P = 5, Q = 1, R = 2, S = 4. Statement I: 6 = 6. Statement II: 9 is more than 3. Both hold, and now P is more than Q.
4. Same statements, different answers: even together they are not enough. (d).
Answer as per the official UPSC answer key.
What is the rightmost digit preceding the zeros in the value of 3030?
Answer (d) & explanation
The digit before the zeros is 9 (d). Step 1: 30^30 = 3^30 × 10^30. The 10^30 gives 30 zeros, so the digit just before them is the unit digit of 3^30. Step 2: unit digits of powers of 3 repeat in a cycle of four: 3, 9, 7, 1. Step 3: divide 30 by 4: remainder 2. So take the second digit in the cycle: 9. Options (a) 1, (b) 3 and (c) 7 are the other digits in the cycle.
Tip: for unit digits of powers, find the cycle (most digits repeat every 4). Divide the power by 4 and use the remainder; a remainder of 0 means the last digit of the cycle.
Answer as per the official UPSC answer key.
Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?
Answer (d) & explanation
1. Start with z. If z = 2, then 2y > 6 means y ≥ 4 and x > 8: impossible. So z = 1.
2. With z = 1, 2y > 3 gives y ≥ 2. y = 2 needs x > 4: x = 5, 6, 7. y = 3 needs x > 6: x = 7. y = 4 needs x > 8: none.
3. Four triplets: (5, 2, 1), (6, 2, 1), (7, 2, 1), (7, 3, 1).
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 Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : What is the time required to download the software?
Statement-I : The size of the software is 12 megabytes.
Statement-II : The transfer rate is 2·4 kilobytes per second.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (c) & explanation
Both statements together are needed (c). Step 1: download time = size ÷ transfer rate. Step 2: statement I gives only the size (12 MB). Statement II gives only the rate (2.4 KB per second). Neither alone gives a time. Step 3: together they give one definite time (about 12 × 1024 ÷ 2.4 seconds, roughly 85 minutes). So (c). Options (a), (b) and (d) fail.
Tip: in data sufficiency you only need to know that one answer is fixed; you need not calculate it. Watch units: MB and KB differ by 1024 (or 1000).
Answer as per the official UPSC answer key.
A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?
Answer (c) & explanation
The men must increase by 20% (c). Step 1: total work = men × days. So if M men take 6k days, M × 6k = M′ × 5k, where M′ is the new number of men. Step 2: M′ = 6M/5 = 1.2M. Step 3: the increase is 0.2M, that is 20%. Note that k cancels out, so its value does not matter. Option (b), 16.67%, is the fall in days (1k out of 6k), a common mix-up. Options (a) and (d) are wrong.
Tip: men and days are inversely related. If days go from 6 to 5, men go from 5 to 6, an increase of 1 on 5 = 20%. Always take the percentage on the old value.
(b) is the trap: 50/3% is the cut in days for the reverse change, not the rise in men.
UPSC repeats traps like this year after year. The PYQ Book gathers every trap in one place, so you see them coming. Try the free sample
Answer as per the official UPSC answer key.
Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements :
- 1. (p − r)2(qs) is even.
- 2. (q − s)q2s is even.
- 3. (q + r)2(p + s) is odd.
Which of the statements given above are correct?
Answer (d) & explanation
All three statements are correct (d). Step 1: rule: a product is even if any factor is even; it is odd only if all factors are odd. p, q are odd; r, s are even. Step 2: statement 1: (p − r)² × q × s. s is even, so the product is even. Statement 2: (q − s) × q² × s: again s makes it even. Step 3: statement 3: q + r = odd + even = odd, so its square is odd. p + s = odd + even = odd. Odd × odd = odd. So all three are true, and options (a), (b) and (c) fail.
Tip: odd ± even = odd; odd ± odd = even. One even factor makes a whole product even.
Answer as per the official UPSC answer key.
Read the passage
Unlike religion and science, poetry does not posit or expect any belief in absolute truths. Those forces or individuals who claim to have absolute truths in their grasp tend to turn dictatorial and tyrannical. Truth usually does not admit any contradictions or imperfections. It is unitarian. It is, therefore, not of much use for poetry. Poetry abides by the plurality of life and existence. Perhaps poetry follows reality which is plural, anachronistic, full of contradictions. Against the tyranny of truth, poetry remains a partisan of democratic reality. Against the arrogance of power, wealth and hierarchy, poetry proposes both humility and defiance.
Which one of the following statements best reflects the most logical and rational message conveyed by the above passage?
Answer (d) & explanation
The message is that poetry is a form of dynamic resistance against tyranny and bigotry (d). Step 1: the passage says those who claim absolute truth turn "dictatorial and tyrannical". Step 2: poetry stands "against the tyranny of truth" and, against power and hierarchy, offers "humility and defiance". Defiance against power is resistance: (d). Step 3: option (a) narrows the idea to human imperfection. Option (b), poetry is "anathema to truth", and (c), poetry is only feeling, misstate it; the passage says poetry follows plural reality, not that it hates truth.
Tip: the closing lines often carry the main message. Words like "against" and "defiance" point to resistance.
Answer as per the official UPSC answer key.
421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?
Answer (c) & explanation
Three numbers work as the divisor (c). Step 1: the divisor must leave remainder 1 for both, so it must divide 421 − 1 = 420 and 427 − 1 = 426. Step 2: it must divide their HCF. 426 − 420 = 6, and 6 divides both, so HCF = 6. Divisors of 6: 1, 2, 3, 6. Step 3: a remainder of 1 needs a divisor greater than 1 (dividing by 1 leaves 0). So only 2, 3 and 6 remain: three numbers. Option (d), 4, wrongly counts 1.
Tip: the remainder must always be smaller than the divisor. That rule quietly removes small divisors in such questions.
counting 1 as a divisor gives (d). Dividing by 1 leaves remainder 0, not 1.
Answer as per the official UPSC answer key.
The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples. Consider the following statements :
- 1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.
- 2. The total cost of one orange and one mango is equal to the cost of one apple.
Which of the statements given above is/are correct?
Answer (c) & explanation
Both statements are correct (c). Step 1: write o, m, a for the prices. 4o + 6m + 8a = 2(o + 2m + 5a) = 2o + 4m + 10a. Step 2: simplify: 2o + 2m = 2a, so o + m = a. One orange and one mango cost the same as one apple: statement 2 is right. Step 3: statement 1: (3o + 5m + 9a) − (4o + 6m + 8a) = a − o − m = 0. The two totals are equal, so statement 1 is right too. Options (a), (b) and (d) fail.
Tip: form one equation and simplify it first. Then test each statement by subtracting the two sides and checking for zero.
Answer as per the official UPSC answer key.
A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years back”. If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
Answer (a) & explanation
The age difference is 30 years (a). Step 1: let the father be F and the son S. "n years back I was as old as you are now" means F − n = S, so n = F − S. Step 2: "my age is four times your age n years back": F = 4(S − n) = 4(S − F + S) = 4(2S − F). So 5F = 8S, giving F : S = 8 : 5. Step 3: 8 + 5 = 13 parts = 130 years, so one part = 10. F = 80, S = 50, difference = 30 years. Check: n = 30; the son 30 years back was 20, and 4 × 20 = 80. Options (b), (c) and (d) fail.
Tip: in age puzzles, note that the age difference never changes. Turn each sentence into one equation.
Answer as per the official UPSC answer key.
Read the passage
In a robust democracy, reality, howsoever inconvenient it may be, finds its expression both in the speech of political leaders and the other social forms of assertion. The existence of the real has to be transparent, both through its circulation in and by the media as well as its argumentative articulation in deliberative democracy. A normatively responsible media through its communication effect has the responsibility to circulate the content of reality without distortion.
Which one of the following statements best reflects the crux of the above passage?
Answer (a) & explanation
The crux is that responsible media should not distort reality in an ideal democracy (a). Step 1: the passage says in a robust democracy, reality, "howsoever inconvenient", must be expressed openly by leaders and society. Step 2: its last sentence says a responsible media must "circulate the content of reality without distortion". That is (a). Step 3: option (b) calls fake news inherent, and (d) says media and leaders cannot be controlled: both are negative and unsupported. Option (c), no restrictions at all on speech, is too broad; the passage talks about truthful reporting, not unlimited freedom.
Tip: the last sentence of a short passage often states its crux. In India, Article 19(1)(a) protects free speech, with reasonable limits under Article 19(2).
Answer as per the official UPSC answer key.
X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?
Answer (c) & explanation
The minimum time is 6 hours 45 minutes (c). Step 1: work done per hour: X = 1/6, Y = 1/8, Z = 1/8. To finish fast, use X, the fastest, as often as possible: every other hour, since no one can work two hours in a row. Step 2: order X, Y, X, Z, X, Y for 6 hours: 3 × 1/6 + 3 × 1/8 = 1/2 + 3/8 = 7/8 done. Step 3: 1/8 is left. Hour 7 can be X again: (1/8) ÷ (1/6) = 3/4 hour = 45 minutes. Total 6 h 45 min. Options (a) and (b) are too short; (d) wastes time.
Tip: in "one worker at a time" questions, give the fastest worker every slot the rule allows, and let the fastest finish the leftover bit.
Answer as per the official UPSC answer key.