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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)
Timed · 30 minutes a set Practise Arithmetic: percentage, ratio, averages, time & work as timed tests 7 sets of about 20 questions with UPSC's CSAT marking. Start practising

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);” Sub-topics in the detailed syllabus →

Showing 121–132 of 132, newest first.

CSAT 2016 · Q30

X-Ray · Core #5 Easy

अनिता की गणित परीक्षा में 70 प्रश्न समान अंकों के थे जिनमें 10 अंकगणित के, 30 बीजगणित के और 30 ज्यामिति के थे। यद्यपि उसने अंकगणित के 70%, बीजगणित के 40% और ज्यामिति के 60% प्रश्नों का सही उत्तर दिया, वह परीक्षा में सफल नहीं हुई क्योंकि उसके अंक 60% से कम थे। उसने कितने और प्रश्नों के सही उत्तर दिए होते, जिससे कि उसे 60% का पास प्राप्तांक मिल गया होता ?

Read this question in English

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:

(a) 1 · (b) 5 · (c) 7 · (d) 9

उत्तर और व्याख्या · explanation in English

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

एक कक्षा में 18 लड़के बहुत लम्बे हैं। यदि ये लड़के, लड़कों की कुल संख्या के तीन-चौथाई हैं और लड़कों की संख्या कक्षा के छात्रों की कुल संख्या की दो-तिहाई है, तो कक्षा में लड़कियों की संख्या क्या है ?

Read this question in English

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?

(a) 6 · (b) 12 · (c) 18 · (d) 21

उत्तर और व्याख्या · explanation in English

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

किसी कम्पनी के सभी कर्मचारियों का मासिक औसत वेतन रु. 5,000 था। पुरुष एवं महिला कर्मचारियों को प्रदत्त मासिक औसत वेतन क्रमशः रु. 5,200 तथा रु. 4,200 था। कम्पनी में कार्यरत पुरुष कर्मचारियों की प्रतिशतता क्या है ?

Read this question in English

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:

(a) 75% · (b) 80% · (c) 85% · (d) 90%

उत्तर और व्याख्या · explanation in English

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

दो संख्याएं X और Y, किसी तीसरी संख्या Z से क्रमशः 20% तथा 28% कम हैं। संख्या Y संख्या X से कितने प्रतिशत कम है ?

Read this question in English

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?

(a) 12% · (b) 10% · (c) 9% · (d) 8%

उत्तर और व्याख्या · explanation in English

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

5 सदस्यों वाले परिवार में 3 वर्ष पूर्व सभी सदस्यों की आयु का योग 80 वर्ष था। इस परिवार की 3 वर्ष पूर्व जो औसत आयु थी, आज भी वही है क्योंकि अन्तःस्थ अवधि में परिवार में एक शिशु की वृद्धि हुई। शिशु की आयु क्या है ?

Read this question in English

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?

(a) 6 months · (b) 1 year · (c) 2 years · (d) 2 years and 6 months

उत्तर और व्याख्या · explanation in English

Answer: (b) 1 वर्ष

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

दो व्यक्तियों की सम्पूर्ण वेतन-लब्धियां बराबर हैं, पर उनमें से एक को अपने मूल वेतन का 65% भत्तों के रूप में मिलता है जबकि दूसरे को मूल वेतन का 80% भत्तों के रूप में मिलता है। पहले व्यक्ति के मूल वेतन का, दूसरे व्यक्ति के मूल वेतन से क्या अनुपात है ?

Read this question in English

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:

(a) 16: 13 · (b) 5: 4 · (c) 7: 5 · (d) 12: 11

उत्तर और व्याख्या · explanation in English

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

राम और श्याम किसी कार्य को करने के लिए चार दिन एक साथ काम करते हैं और 60% कार्य पूरा करते हैं। तब राम छुट्टी पर चला जाता है और श्याम काम को पूरा करने में आठ दिन और लगाता है। राम को अकेले कार्य पूरा करने में कितने दिन लगते ?

Read this question in English

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?

(a) 6 days · (b) 8 days · (c) 10 days · (d) 11 days

उत्तर और व्याख्या · explanation in English

Answer: (c) 10 दिन

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

X-Ray · Core #5 Easy

A और B पैदल चलते हुए एक वृत्ताकार पार्क का चक्कर लगाते हैं। वे दोनों प्रातः 8 बजे एक ही बिंदु से विपरीत दिशाओं में चलना शुरू करते हैं। A और B की चाल क्रमशः 2 चक्कर प्रति घंटा व 3 चक्कर प्रति घंटा है। प्रातः 8 बजे के बाद तथा प्रातः 9.30 बजे से पूर्व वे कितनी बार एक-दूसरे के सामने से गुजरेंगे ?

Read this question in English

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.?

(a) 7 · (b) 6 · (c) 5 · (d) 8

उत्तर और व्याख्या · explanation in English

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, किसी कार्य के 25% भाग को 30 दिनों में करता है; X उस कार्य के 1/4 भाग को 10 दिनों में करता है। Y उस कार्य के 40% भाग को 40 दिनों में करता है और Z उस कार्य के 1/3 भाग को 13 दिनों में करता है। कार्य को सबसे पहले कौन पूरा करेगा ?

Read this question in English

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?

(a) W · (b) X · (c) Y · (d) Z

उत्तर और व्याख्या · explanation in English

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

5 व्यक्तियों के किसी एक परिवार में प्रति व्यक्ति औसत आय रु॰ 10,000 प्रति मास है। उसी परिवार में प्रति व्यक्ति औसत आय क्या होगी यदि किसी एक व्यक्ति की आय में रु॰ 1,20,000 प्रति वर्ष की वृद्धि हो जाती है ?

Read this question in English

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?

(a) Rs. 12,000 · (b) Rs. 16,000 · (c) Rs. 20,000 · (d) Rs. 34,000

उत्तर और व्याख्या · explanation in English

Answer: (a) रु॰ 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

किसी दौड़ में एक प्रतियोगी को 6 सेब एकत्र करने हैं। ये सेब एक सरल रेखा में किसी ट्रैक पर रखे हुए हैं और ट्रैक के प्रारम्भ में बाल्टी रखी गई है जो कि दौड़ का प्रारम्भ बिंदु है। खेल के नियमानुसार, प्रतियोगी एक बार में केवल एक सेब उठा सकता है और उसे लेकर वापस दौड़ कर उसे बाल्टी में डाल सकता है। बाल्टी से, पहले सेब की दूरी 5 मीटर है तथा बाकी सेब 3-3 मीटर की दूरी पर हैं। यदि प्रतियोगी को बाल्टी में सभी सेब डालने हों तो प्रतियोगी को कुल कितनी दूरी दौड़ कर तय करनी है ?

Read this question in English

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?

(a) 40 m · (b) 50 m · (c) 75 m · (d) 150 m

उत्तर और व्याख्या · explanation in English

Answer: (d) 150 मीटर

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

कोई व्यक्ति किसी खिलौने की अंकित कीमत पर, नगद भुगतान के लिए, 10% छूट देता है फिर भी उसे 10% का लाभ होता है। उस खिलौने की लागत कीमत क्या है, जिसकी अंकित कीमत रु॰ 770 है ?

Read this question in English

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?

(a) Rs. 610 · (b) Rs. 620 · (c) Rs. 630 · (d) Rs. 640

उत्तर और व्याख्या · explanation in English

Answer: (c) रु॰ 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 ·

The Syllabus X-Ray of this topic

1 of its 7 sub-topics is Core

1 Core · 2 High · 4 Steady · 0 Rare

  • Core #5Word problems & equations · 40 questions
  • HighPercentages, profit & loss · 33 questions
  • HighAverages & ages · 19 questions

The X-Ray ranks all 928 sub-topics of the UPSC syllabus by what UPSC has asked since 2016. The 6 CSAT Core sub-topics are behind 50% of CSAT questions.

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