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CSAT · 132 questions

Arithmetic: percentage, ratio, averages, time & work

Every UPSC CSAT question on this topic, 2016–2026, newest first. Tap an option to check yourself; the answer and explanation open below it.

Arithmetic: percentage, ratio, averages, time & work questions per year: 2016: 16, 2017: 11, 2018: 8, 2019: 15, 2020: 15, 2021: 16, 2022: 13, 2023: 2, 2024: 11, 2025: 9, 2026: 16 Asked in 11 of 11 years · most in 2026 (16)

UPSC syllabus: “Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation (charts, graphs, tables, data sufficiency etc. — Class X level);” See the full syllabus →

CSAT 2019 · Q11

Easy

A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?

Answer & explanation

Answer: (d) 37.5%

B weighs 60% of A, but the fall is measured against the larger total A + B. Removing 60 from 160 is a 37.5% reduction, not 60%.

  1. Let A weigh 100. B on top raises the weight by 60%, so B = 60.
  2. Total weight of A and B = 160.
  3. Removing B takes away 60 out of 160.
  4. Reduction = 60/160 × 100% = 37.5%.

Remember · A rise of r% is undone by a fall of r/(100 + r) × 100% — divide by the new, larger base.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q16

Easy

When a runner was crossing the 12 km mark, she was informed that she had completed only 80% of the race. How many kilometres was the runner supposed to run in this event?

Answer & explanation

Answer: (b) 15

12 km is four-fifths of the race, so the full distance is 12 × 5/4 = 15 km.

  1. 12 km = 80% of the race.
  2. Race = 12 × 100/80 = 15 km.
  3. Check: 80% of 15 = 12.

Remember · If x is p% of the whole, the whole is x × 100/p.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q17

Easy

Raju has ₹ 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows ₹ 2000 from a friend. Then

Answer & explanation

Answer: (a) Raju still does not have enough amount to buy the handset.

The handset costs ₹12,000 because ₹9,000 is only three-quarters of the price. With the ₹2,000 loan Raju has ₹11,000, still ₹1,000 short.

  1. ₹9000 is 75% of the price, so the price = 9000 × 100/75 = ₹12000.
  2. After borrowing he has 9000 + 2000 = ₹11000.
  3. 11000 < 12000: he is still ₹1000 short.

Remember · Find the base first (amount ÷ percentage), then compare; don't mix percentages with rupee amounts.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q18

Easy

In 2002, Meenu’s age was one-third of the age of Meera, whereas in 2010, Meenu’s age was half the age of Meera. What is Meenu’s year of birth?

Answer & explanation

Answer: (b) 1994

Writing Meera's 2002 age as three times Meenu's and applying the 'half' relation eight years later gives Meenu's 2002 age as 8, so she was born in 1994.

  1. Let Meenu be m years old in 2002; Meera is then 3m.
  2. In 2010 both are 8 years older: m + 8 = (3m + 8)/2.
  3. 2m + 16 = 3m + 8, so m = 8.
  4. Meenu was 8 in 2002, so she was born in 2002 − 8 = 1994.
  5. Check: 2002 — 8 and 24 (one-third); 2010 — 16 and 32 (half).

Remember · Both ages move by the same number of years; write them with one variable and shift both together.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q19

Easy

Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent ₹ 1300 and Rajesh spent ₹ 1500. If each racket costs three times a ball does, then what is the price of a racket?

Answer & explanation

Answer: (c) ₹ 210

Only the joint spending matters: ₹2,800 buys 10 balls and 10 rackets, which is the cost of 40 balls. So a ball is ₹70 and a racket ₹210.

  1. Total spent = 1300 + 1500 = ₹2800 for 10 balls and 10 rackets.
  2. Let a ball cost b; a racket costs 3b.
  3. 10b + 10 × 3b = 40b = 2800, so b = 70.
  4. Racket = 3 × 70 = ₹210.
  5. Check: 10 × 70 + 10 × 210 = 700 + 2100 = 2800.

Remember · When the split between buyers is irrelevant, add the spends and solve for the combined purchase.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q20

Medium

In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct?

  1. 1.At least 30 Indian participants are vegetarian.
  2. 2.At least 10 Indian participants are non-vegetarian.

Select the correct answer using the codes given below:

Answer & explanation

Answer: (c) Both 1 and 2

Only 30 participants are not Indian. Even if all of them were vegetarian, at least 60 − 30 = 30 vegetarians are Indian; and even if all 30 were non-vegetarian, at least 40 − 30 = 10 non-vegetarians are Indian.

  1. Non-Indians = 100 − 70 = 30; non-vegetarians = 100 − 60 = 40.
  2. Fewest Indian vegetarians: make all 30 non-Indians vegetarian → Indian vegetarians = 60 − 30 = 30.
  3. Fewest Indian non-vegetarians: make all 30 non-Indians non-vegetarian → Indian non-vegetarians = 40 − 30 = 10.
  4. Both minimums hold, so both statements are correct.
  5. Check: 70 + 60 − 100 = 30 and 70 + 40 − 100 = 10.
  • ✓ 1. At most 30 vegetarians can be non-Indian, so at least 30 of the 60 vegetarians are Indian.
  • ✓ 2. At most 30 non-vegetarians can be non-Indian, so at least 10 of the 40 non-vegetarians are Indian.

Remember · For a guaranteed overlap, push the other group to the extreme: minimum overlap = A + B − total.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q31

Easy

All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data?

  1. 1.40% members went for shopping as well as sightseeing.
  2. 2.20% members went for only shopping.

Select the correct answer using the code given below:

Answer & explanation

Answer: (a) 1 only

Since 10% only rested, 90% went shopping, sightseeing or both. Shopping and sightseeing together add up to 130%, so 40% did both, and 80 − 40 = 40% did only shopping — not 20%.

  1. Members who went out = 100% − 10% = 90%.
  2. Both = 80% + 50% − 90% = 40%.
  3. Only shopping = 80% − 40% = 40%.
  4. Check: only shopping 40 + only sightseeing 10 + both 40 + rest 10 = 100.
  • ✓ 1. 80 + 50 − 90 = 40% did both.
  • ✗ 2. Only shopping is 80 − 40 = 40%, not 20%.

Remember · Both = A + B − (at least one); get 'at least one' by removing the 'neither' group first.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q34

Easy

In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored?

Answer & explanation

Answer: (b) 380

B's shortfall of 5% is measured on A's marks and equals the 20-mark gap, so A has 400 and B 380.

  1. B = A − 20, and B = 95% of A.
  2. So 5% of A = 20, giving A = 400.
  3. B = 400 − 20 = 380.
  4. Check: 95% of 400 = 380.

Remember · When a percentage gap equals a known difference, that difference is the percentage of the base.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q36

Medium

X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?

Answer & explanation

Answer: (b) 25

While X runs 1000 m, Y runs 960 m and Z 936 m. So while Y runs 1000 m, Z runs 1000 × 936/960 = 975 m, and Y can give Z a start of 25 m.

  1. X gives Y 40 m: while X runs 1000 m, Y runs 960 m.
  2. X gives Z 64 m: in the same time Z runs 936 m.
  3. Speed ratio Y : Z = 960 : 936.
  4. While Y runs 1000 m, Z runs 1000 × 936/960 = 975 m.
  5. Start Y gives Z = 1000 − 975 = 25 m.

Remember · Turn 'starts' into distances run in the same time, then scale to the new race length.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q38

Easy

Ena was born 4 years after her parents’ marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena’s father get married?

Answer & explanation

Answer: (b) 23 years

Ena is 13, her mother 37 and her father 40. The marriage took place 13 + 4 = 17 years ago, when the father was 40 − 17 = 23.

  1. Ena = 13; mother = 13 + 24 = 37; father = 37 + 3 = 40.
  2. The marriage was 4 years before Ena's birth: 13 + 4 = 17 years ago.
  3. Father's age at marriage = 40 − 17 = 23 years.

Remember · Fix everyone's present age first, then move all of them back by the same number of years.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q39

Easy

Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered?

Answer & explanation

Answer: (b) 20%

The same money buys 10 handsets instead of 8, so the new price is 8/10 of the old one — a 20% discount. 25% is the rise in quantity, not the fall in price.

  1. Let the price be ₹100; Rakesh has 8 × 100 = ₹800.
  2. ₹800 now buys 10 handsets, so the discounted price = ₹80.
  3. Discount = (100 − 80)/100 × 100% = 20%.

Remember · With fixed money, price × quantity is constant: quantities 8 : 10 mean prices 10 : 8.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q40

Easy

The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are

Answer & explanation

Answer: (b) 39.7

The total was overstated by 83 − 53 = 30 marks, so the correct total is 3970 and the mean is 39.7.

  1. Recorded total = 100 × 40 = 4000.
  2. Excess from the misreading = 83 − 53 = 30.
  3. Correct total = 4000 − 30 = 3970; correct mean = 3970/100 = 39.7.
  4. Shortcut: the mean falls by 30/100 = 0.3.

Remember · One wrong entry shifts the mean by (wrong − right) ÷ n.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q52

Easy

In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is

Answer & explanation

Answer: (b) 9

Twelve people read at least one language. French and English readers add to 15, so 3 read both, and 12 − 3 = 9 read exactly one.

  1. At least one language = 15 − 3 = 12.
  2. Both = 7 + 8 − 12 = 3.
  3. Exactly one = 12 − 3 = 9 (French only 4, English only 5).

Remember · Exactly one = (at least one) − (both); get 'both' from A + B − (at least one).

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q55

Easy

A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother?

Answer & explanation

Answer: (d) 54 kg

Children plus mother weigh 150 kg and children plus father 156 kg, so the father is 6 kg heavier than the mother. With the father at 60 kg, the mother weighs 54 kg.

  1. Children + mother = 3 × 50 = 150 kg.
  2. Children + father = 3 × 52 = 156 kg.
  3. Father − mother = 156 − 150 = 6 kg.
  4. Mother = 60 − 6 = 54 kg.
  5. Check: children = 156 − 60 = 96, and 96 + 54 = 150.

Remember · When two averages share members, subtract the totals — the shared part cancels.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2019 · Q69

Easy

Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is

Answer & explanation

Answer: (d) 30 units

The single-digit odd primes are 3, 5 and 7, so the first piece is 5 units. With the third piece T, the second is 5 + T/3 and T = 10 + T/3, so T = 15, the second piece is 10 and the sheet is 30 units.

  1. Single-digit odd primes: 3, 5, 7; average = 15/3 = 5, so the first piece = 5.
  2. Let the third piece be T; the second = 5 + T/3.
  3. Third = first + second: T = 5 + 5 + T/3 → 2T/3 = 10 → T = 15.
  4. Second = 5 + 15/3 = 10.
  5. Sheet = 5 + 10 + 15 = 30 units.
  6. Check: the third piece (15) equals 5 + 10.

Remember · If one part equals the sum of the others, the whole is twice that part.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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