Minimalist IAS
CSAT

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 2016 · Q14

Easy

There are some nectar-filled flowers on a tree and some bees are hovering on it. If one bee lands on each flower, one bee will be left out. If two bees land on each flower, one flower will be left out. The number of flowers and bees respectively are:

Answer & explanation

Answer: (c) 3 and 4

One bee per flower leaves a bee over, so bees = flowers + 1. Two per flower leaves a flower empty, so bees = 2 × (flowers − 1). Together these give 3 flowers and 4 bees.

  1. Let f = flowers and b = bees.
  2. One bee per flower, one bee left: b = f + 1.
  3. Two bees per flower, one flower left: b = 2(f − 1).
  4. f + 1 = 2f − 2, so f = 3 and b = 4.
  5. Check: 4 bees on 3 flowers, one each, leaves 1 bee; two each fills 2 flowers and leaves 1 flower empty.

Remember · Turn each 'left over' condition into an equation — or simply test each option against both conditions.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q20

Easy

There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per day out of which 5% are unfit for sale. In how many days will the order be completed?

Answer & explanation

Answer: (c) 20

Only 95% of each day's 1000 units can be sold, which is 950 units a day. The order of 19000 therefore takes 19000 ÷ 950 = 20 days.

  1. Usable output per day = 95% of 1000 = 950.
  2. Days needed = 19000 ÷ 950 = 20.
  3. Check: 20 × 950 = 19000.

Remember · Divide the order by the usable output per day, not the gross output.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q26

Easy

A class starts at 11:00 am and lasts till 2:27 pm. Four periods of equal duration are held during this interval. After every period, a rest of 5 minutes is given to the students. The exact duration of each period is:

Answer & explanation

Answer: (a) 48 minutes

The class lasts 207 minutes. Four periods have three 5-minute rests between them, since the last period ends the class, so each period is (207 − 15) ÷ 4 = 48 minutes.

  1. 11:00 am to 2:27 pm = 3 h 27 min = 207 minutes.
  2. Four periods have three rests between them: 3 × 5 = 15 minutes.
  3. Teaching time = 207 − 15 = 192 minutes; each period = 192 ÷ 4 = 48 minutes.
  4. Check: 48 + 5 + 48 + 5 + 48 + 5 + 48 = 207.

Remember · n periods in a block have n − 1 breaks between them: subtract the breaks, then divide by n.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q28

Easy

30 g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar was mixed in 280 ml of water in vessel B and 20 g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is:

Answer & explanation

Answer: (d) less sweet than that in C

Sweetness depends on sugar per unit of water. A has 30/180 = 1/6, B has 40/280 = 1/7 and C has 20/100 = 1/5 g per ml, so B is the weakest and is less sweet than C.

  1. Sugar per ml of water — A: 30/180 = 1/6; B: 40/280 = 1/7; C: 20/100 = 1/5.
  2. 1/7 < 1/6 < 1/5, so B is the least sweet of the three.
  3. So B is less sweet than C (and than A); (a), (b) and (c) are false.

Remember · Compare concentrations as ratios; reducing each to a simple fraction (1/5, 1/6, 1/7) makes the order obvious.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q30

Easy

Anita's mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is:

Answer & explanation

Answer: (b) 5

She answered 7 + 12 + 18 = 37 problems correctly, while a pass needs 60% of 70 = 42. She needed 5 more correct answers.

  1. Correct answers: 70% of 10 = 7; 40% of 30 = 12; 60% of 30 = 18. Total = 37.
  2. Pass mark: 60% of 70 = 42 questions.
  3. More needed: 42 − 37 = 5.

Remember · With equal marks per question, turn every percentage into a count of questions and compare counts.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q31

Easy

In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

Answer & explanation

Answer: (b) 12

Eighteen is three-fourths of the boys, so there are 24 boys. They are two-thirds of the class, so the class has 36 students and 12 of them are girls.

  1. Boys = 18 ÷ 3/4 = 24.
  2. Class = 24 ÷ 2/3 = 36.
  3. Girls = 36 − 24 = 12.

Remember · Work back from the part to the whole one fraction at a time: whole = part ÷ fraction.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q33

Easy

The monthly average salary paid to all the employees of a company was Rs. 5000. The monthly average salary paid to male and female employees was Rs. 5200 and Rs. 4200 respectively. Then the percentage of males employed in the company is:

Answer & explanation

Answer: (b) 80%

The overall average of Rs. 5000 is Rs. 200 below the men's average and Rs. 800 above the women's. So men and women are in the ratio 800 : 200 = 4 : 1, and men are 80% of the staff.

  1. Let the share of men be m; women are 1 − m.
  2. 5200m + 4200(1 − m) = 5000, so 1000m = 800 and m = 0.8.
  3. Men = 80%.
  4. Check by alligation: distances 5200 − 5000 = 200 and 5000 − 4200 = 800; men : women = 800 : 200 = 4 : 1.

Remember · Alligation: each group's share is proportional to the other group's distance from the overall average.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q37

Easy

Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X?

Answer & explanation

Answer: (b) 10%

Take Z = 100: then X = 80 and Y = 72. Y is 8 less than X, and measured against X that is 8/80 = 10%.

  1. Let Z = 100. Then X = 80 and Y = 72.
  2. Y is less than X by 80 − 72 = 8.
  3. As a percentage of X: 8/80 × 100 = 10%.

Remember · 'By what % is Y less than X' uses X as the base. Taking the reference number as 100 avoids fractions.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q51

Easy

The sum of the ages of 5 members comprising a family, 3 years ago was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby?

Answer & explanation

Answer: (b) 1 year

The five members now total 80 + 15 = 95 years. With the baby, six people must total 6 × 16 = 96 years to keep the average at 16, so the baby is 1 year old.

  1. Three years ago: 5 members, total 80, average 16.
  2. Today the same 5 total 80 + 5 × 3 = 95.
  3. Today 6 members average 16: total 6 × 16 = 96.
  4. Baby's age = 96 − 95 = 1 year.

Remember · Age totals grow by (number of people × years passed); compare the required total with the grown total.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q52

Easy

The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is:

Answer & explanation

Answer: (d) 12: 11

Equal totals mean 165% of the first person's basic pay equals 180% of the second's. So the basic pays are in the ratio 180 : 165 = 12 : 11.

  1. First: basic x, total 1.65x. Second: basic y, total 1.80y.
  2. 1.65x = 1.80y, so x : y = 180 : 165 = 12 : 11.
  3. Check: 12 × 1.65 = 19.8 and 11 × 1.80 = 19.8.

Remember · If a% of X equals b% of Y, then X : Y = b : a.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q60

Easy

Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?

Answer & explanation

Answer: (c) 10 days

Together they do 60% in 4 days, i.e. 15% a day. Shyam alone does the other 40% in 8 days, i.e. 5% a day. So Ram does 10% a day and would need 10 days alone.

  1. Together: 60% in 4 days = 15% a day.
  2. Shyam alone: 40% in 8 days = 5% a day.
  3. Ram = 15% − 5% = 10% a day, so 100 ÷ 10 = 10 days.

Remember · Turn work into per-day percentages; rates simply add when people work together.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q75

Easy

A and B walk around a circular park. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 8.00 a.m. and before 9.30. a.m.?

Answer & explanation

Answer: (a) 7

Walking in opposite directions they together cover 5 rounds an hour, so they meet every 12 minutes. In the 90 minutes up to 9:30 they cross at 12, 24, …, 84 minutes — 7 times.

  1. In opposite directions their speeds add: 2 + 3 = 5 rounds an hour.
  2. They meet each time they together complete one round: every 60 ÷ 5 = 12 minutes.
  3. 8:00 to 9:30 is 90 minutes: meetings at 12, 24, 36, 48, 60, 72 and 84 minutes.
  4. That is 7 crossings; the next would be at 96 minutes, after 9:30.

Remember · Opposite directions on a circular track: crossings = combined rounds covered, counting only whole rounds completed within the time.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q76

Easy

W can do 25% of a work in 30 days, X can do 1/4 of the work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first?

Answer & explanation

Answer: (d) Z

Scaling each part-job up to the whole work: W needs 120 days, X 40, Y 100 and Z 39. Z finishes first.

  1. W: 25% in 30 days → 30 ÷ 1/4 = 120 days.
  2. X: 1/4 in 10 days → 40 days.
  3. Y: 40% in 40 days → 40 ÷ 2/5 = 100 days.
  4. Z: 1/3 in 13 days → 39 days — the fastest.

Remember · Convert every rate to days for the whole job (days ÷ fraction done) before comparing.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q77

Easy

The average monthly income of a person in a certain family of 5 is Rs. 10,000. What will be the average monthly income of a person in the same family if the income of one person increased by Rs. 1,20,000 per year?

Answer & explanation

Answer: (a) Rs. 12,000

A rise of Rs. 1,20,000 a year is Rs. 10,000 a month. Shared across 5 people it lifts the monthly average by Rs. 2,000, from Rs. 10,000 to Rs. 12,000.

  1. Family's monthly income = 5 × Rs. 10,000 = Rs. 50,000.
  2. Rs. 1,20,000 a year = Rs. 10,000 a month.
  3. New average = (50,000 + 10,000) ÷ 5 = Rs. 12,000.

Remember · Put all figures in the same time unit first; the average then rises by the increase divided by the number of people.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q78

Easy

In a race, a competitor has to collect 6 apples which are kept in a straight line on a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is 5 meters from the first apple and all other apples are placed 3 meters apart?

Answer & explanation

Answer: (d) 150 m

The apples lie 5, 8, 11, 14, 17 and 20 m from the bucket, and he must run to each and back. The total is 2 × (5 + 8 + 11 + 14 + 17 + 20) = 2 × 75 = 150 m.

  1. Distances from the bucket: 5, 8, 11, 14, 17 and 20 m.
  2. Each apple needs a run there and back: 2 × distance.
  3. Total = 2 × (5 + 8 + 11 + 14 + 17 + 20) = 2 × 75 = 150 m.

Remember · One-at-a-time fetching doubles every distance; add the distances as a series (number of terms × average).

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q80

Easy

A person allows a 10% discount for cash payment from the marked price of a toy and still he makes a 10% gain. What is the cost price of the toy which is marked Rs. 770?

Answer & explanation

Answer: (c) Rs. 630

After a 10% discount the toy sells for Rs. 693. That price already includes a 10% gain, so the cost price is 693 ÷ 1.1 = Rs. 630.

  1. Selling price = 90% of Rs. 770 = Rs. 693.
  2. Cost price × 1.1 = 693, so cost price = Rs. 630.
  3. Check: 630 × 1.1 = 693.

Remember · Chain the percentages: marked price × (1 − discount) = cost price × (1 + gain).

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

From the UPSC Blog

Other CSAT skills