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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 →

CSAT 2021 · Q7

Medium

1 जनवरी, 2021 से वर्ष के mवें दिन पेट्रोल का मूल्य (रुपए प्रति लीटर में) 80 + 0·1m है, जहाँ m = 1, 2, 3, ..., 100 है और तत्पश्चात अचर रहता है । वहीं दूसरी ओर, वर्ष 2021 के nवें दिन डीज़ल का मूल्य (रुपए प्रति लीटर में), n के किसी भी मान के लिए 69 + 0·15n है । वर्ष 2021 की किस तिथि को इन दोनों ईंधनों का मूल्य एकसमान होगा ?

Read this question in English

From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1m, where m = 1, 2, 3, ..., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is 69 + 0.15n for any n. On which date in the year 2021 are the prices of these two fuels equal?

(a) 21st May · (b) 20th May · (c) 19th May · (d) 18th May

उत्तर और व्याख्या · explanation in English

Answer: (b) 20 मई

The two formulas never meet within the first 100 days, after which petrol stays at ₹90. Diesel reaches ₹90 on day 140, and day 140 of 2021 (not a leap year) is 20 May.

  1. While both formulas run (days 1–100): 80 + 0.1m = 69 + 0.15m gives 0.05m = 11, so m = 220 — outside 1 to 100, so no match in this period.
  2. From day 100 onwards petrol stays at 80 + 0.1 × 100 = ₹90.
  3. Diesel reaches ₹90 when 69 + 0.15n = 90, i.e. 0.15n = 21, so n = 140.
  4. Days up to 30 April: 31 + 28 + 31 + 30 = 120, so day 140 is the 20th day of May — 20 May.
  5. Check: on day 140 diesel = 69 + 0.15 × 140 = 69 + 21 = ₹90, equal to petrol.

Remember · For prices defined piece by piece, test each piece separately; then turn the day number into a date month by month.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q8

X-Ray · Core #5 Easy

एक हाई स्कूल की जीवविज्ञान की कक्षा ने पूर्वानुमान लगाया कि पशुओं की स्थानीय आबादी प्रत्येक 12 वर्ष में दुगुनी हो जाएगी । किए गए आकलन के अनुसार वर्ष 2021 के आरंभ में पशुओं की आबादी 50 होगी । यदि n वर्षों के पश्चात की आबादी को P से निरूपित किया जाता है, तो निम्नलिखित में से कौन-सा समीकरण, कक्षा द्वारा बनाए गए आबादी के मॉडल को निरूपित करता है ?

Read this question in English

A biology class at high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population?

(a) P = 12 + 50n · (b) P = 50 + 12n · (c) P = 50 (2)^(12n) · (d) P = 50 (2)^(n/12)

उत्तर और व्याख्या · explanation in English

Answer: (d) P = 50 (2)^(n/12)

Doubling every 12 years is exponential growth: after n years the population has doubled n/12 times, so P = 50 × 2^(n/12). Putting n = 0 and n = 12 (giving 50 and 100) confirms it and rules out the other options.

  1. Doubling every 12 years means multiplying by 2 once for each 12-year block.
  2. In n years there are n/12 such blocks, so P = 50 × 2^(n/12).
  3. Check: n = 0 gives 50; n = 12 gives 100; n = 24 gives 200 — doubling every 12 years.
  4. Options (a) and (b) add a fixed number each year (linear growth); (c) gives 50 × 2¹² at n = 1, far too fast.

Remember · Test formula options by plugging in simple values — the start (n = 0) and one full period.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q9

Easy

एक कक्षा में, 60% विद्यार्थी भारत से हैं और विद्यार्थियों का 50% लड़कियाँ हैं । यदि भारतीय विद्यार्थियों में 30% लड़कियाँ हैं, तो विदेशी विद्यार्थियों में कितने प्रतिशत लड़के हैं ?

Read this question in English

In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys?

(a) 45% · (b) 40% · (c) 30% · (d) 20%

उत्तर और व्याख्या · explanation in English

Answer: (d) 20%

Take 100 students: 60 Indian and 40 foreign, with 50 girls. Indian girls are 18, so foreign girls are 32 and foreign boys only 8 — that is 8 out of 40 foreign students, or 20%.

  1. Take 100 students: 60 Indian, 40 foreign; 50 girls in all.
  2. Indian girls = 30% of 60 = 18.
  3. Foreign girls = 50 − 18 = 32, so foreign boys = 40 − 32 = 8.
  4. Share of boys among foreign students = 8/40 = 20%.
  5. Check: boys = 50; Indian boys 60 − 18 = 42 plus foreign boys 8 = 50.

Remember · Assume a total of 100 and fill a 2 × 2 table; then divide by the base the question names (here, foreign students).

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q16

X-Ray · Core #5 Medium

एक बालक गेंद से खेल रहा है और वह गेंद को 1·5 m की ऊँचाई से गिराता है । प्रत्येक बार जब भी गेंद ज़मीन से टकराती है, तो वह पूर्ववर्ती ऊँचाई की 4/5 ऊँचाई तक उछाल लेती है । यदि पूर्ववर्ती ऊँचाई 50 cm से कम है, तो गेंद नहीं उछलती है । गेंद की उछाल रुकने से पूर्व, गेंद कितनी बार ज़मीन से टकराती है ?

Read this question in English

A boy plays with a ball and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing?

(a) 4 · (b) 5 · (c) 6 · (d) 7

उत्तर और व्याख्या · explanation in English

Answer: (b) 5

Why not the tempting option · UPSC's key is 5. A very literal reading of 'previous height' lets the ball rise once more, to 49.15 cm, and touch the ground a sixth time; but that final contact is the ball coming to rest, not a hit before it stops bouncing, so 5 remains the better count. In the exam, stop at the first height that breaks the threshold and do not add the final landing.

Each bounce reaches 4/5 of the previous height: 150 → 120 → 96 → 76.8 → 61.44 cm. The next rise would be only 49.15 cm, below the 50 cm limit, so the ball does not bounce again; by then it has hit the ground 5 times.

  1. Heights in cm: dropped from 150, the ball rises to 4/5 of each previous height — 120, 96, 76.8, 61.44.
  2. Every rise is preceded by a hit: hits after falling from 150, 120, 96, 76.8 and 61.44 cm — that is 5 hits.
  3. The rise after the 5th hit would be 4/5 × 61.44 = 49.152 cm, below 50 cm, so the ball does not bounce further.
  4. Number of times the ball hits the ground before it stops bouncing = 5.

Remember · List the geometric sequence of heights, stop at the first term that breaks the threshold, and count the hits up to that point; do not add an extra landing after the ball has stopped bouncing.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 1 Oct 2026 (how we verify). Permalink ·

CSAT 2021 · Q29

Medium

एक व्यक्ति X, स्थान A से तथा एक अन्य व्यक्ति Y, स्थान B से एक ही समय पर एक-दूसरे की ओर चलना आरंभ करते हैं । दोनों स्थानों के बीच की दूरी 15 km है ।

X, 1·5 km/hr की एकसमान चाल से चलता है और Y पहले घंटे में 1 km/hr की एकसमान चाल से, दूसरे घंटे में 1·25 km/hr की एकसमान चाल से तथा तीसरे घंटे में 1·5 km/hr की एकसमान चाल से चलता है और इसी प्रकार आगे भी चलना जारी रखता है ।

निम्नलिखित में से कौन-सा/कौन-से सही है/हैं ?

  1. 1.उन दोनों को मिलने में 5 घंटे का समय लगेगा ।
  2. 2.वे दोनों A तथा B स्थानों के बीचों-बीच मिलेंगे ।

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए :

Read this question in English

A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km.

X walks with a uniform speed of 1.5 km/hr and Y walks with a uniform speed of 1 km/hr in the first hour, with a uniform speed of 1.25 km/hr in the second hour and with a uniform speed of 1.5 km/hr in the third hour and so on.

Which of the following is/are correct?

1. They take 5 hours to meet.

2. They meet midway between A and B.

Select the correct answer using the code given below:

(a) 1 only · (b) 2 only · (c) Both 1 and 2 · (d) Neither 1 nor 2

उत्तर और व्याख्या · explanation in English

Answer: (c) 1 और 2 दोनों

Adding the hourly distances, the two close the 15 km gap exactly at the end of the 5th hour. X walks 5 × 1.5 = 7.5 km and Y walks 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km, so they meet midway — both statements hold.

  1. Distance closed in each hour: 1.5 + 1 = 2.5, then 1.5 + 1.25 = 2.75, then 3, 3.25, 3.5 km.
  2. Running total: 2.5, 5.25, 8.25, 11.5, 15 km — they meet at the end of the 5th hour.
  3. X covers 5 × 1.5 = 7.5 km; Y covers 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km.
  4. Each covers half of 15 km, so they meet midway.
  5. Check: Y's average speed over 5 hours is 7.5 ÷ 5 = 1.5 km/hr, equal to X's speed — hence midway.
  • ✓ 1. The combined distance reaches 15 km exactly after 5 hours.
  • ✓ 2. Both walk 7.5 km in those 5 hours, so the meeting point is the midpoint.

Remember · With speeds changing hour by hour, tabulate the hours; for an arithmetic progression of speeds, the average speed gives a quick check.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q30

X-Ray · Core #5 Easy

एक विद्यार्थी परीक्षा के 6 प्रश्न-पत्रों में बैठता है । प्रत्येक प्रश्न-पत्र के लिए अधिकतम अंक एकसमान हैं । इन प्रश्न-पत्रों में उसके प्राप्तांक 5 : 6 : 7 : 8 : 9 : 10 के अनुपात में हैं । कुल मिलाकर उसने 60% अंक प्राप्त किए । उसने कितने प्रश्न-पत्रों में अधिकतम अंकों के 60% से कम अंक प्राप्त किए ?

Read this question in English

A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5: 6: 7: 8: 9: 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?

(a) 2 · (b) 3 · (c) 4 · (d) 5

उत्तर और व्याख्या · explanation in English

Answer: (b) 3

With equal maximum marks, the overall 60% equals the average of the six papers' shares, and the average of 5 to 10 is 7.5. Only the papers with shares 5, 6 and 7 fall below that level — 3 papers.

  1. Let the marks be 5k, 6k, 7k, 8k, 9k and 10k; the total is 45k.
  2. Since every paper has the same maximum, the overall 60% equals the average paper score: 45k ÷ 6 = 7.5k is 60% of the maximum.
  3. Papers below 7.5k: 5k, 6k and 7k — 3 papers.
  4. Check: if the maximum is 12.5k, the marks are 40%, 48%, 56%, 64%, 72%, 80% — three below 60%.

Remember · When maximum marks are equal, the overall percentage is the average of the paper percentages; compare each paper with the mean.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q35

X-Ray · Core #5 Easy

120 व्यक्तियों के समूह में, 80 भारतीय हैं और शेष विदेशी हैं । इसके अतिरिक्त, इस समूह में 70 व्यक्ति अंग्रेज़ी बोल सकते हैं । ऐसे भारतीयों की संख्या कितनी है जो अंग्रेज़ी बोल सकते हैं ?

Read this question in English

In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English. The number of Indians who can speak English is

(a) 20 · (b) 30 · (c) 30 or less · (d) 30 or more

उत्तर और व्याख्या · explanation in English

Answer: (d) 30 या उससे अधिक

There are only 40 foreigners, so at most 40 of the 70 English speakers can be foreigners. At least 30 must be Indians, and the number could be higher, so the answer is '30 or more'.

  1. Foreigners = 120 − 80 = 40.
  2. Even if all 40 foreigners speak English, at least 70 − 40 = 30 English speakers are Indians.
  3. If all 70 English speakers were Indians, the number would be 70; the data do not fix it.
  4. So the number of Indians who speak English is 30 or more.

Remember · Minimum overlap of two groups = (size of A + size of B) − total; give a range when the data do not fix an exact value.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q37

Medium

दो कक्षाओं A और B में क्रमशः 25 और 30 विद्यार्थी हैं । कक्षा-A में अधिकतम प्राप्तांक 21 है तथा न्यूनतम प्राप्तांक 17 है । कक्षा-B में अधिकतम प्राप्तांक 30 है तथा न्यूनतम प्राप्तांक 22 है । कक्षा-A से 4 विद्यार्थी कक्षा-B में स्थानांतरित किए जाते हैं ।

निम्नलिखित कथनों पर विचार कीजिए :

  1. 1.कक्षा-B का औसत प्राप्तांक निश्चित रूप से घटेगा ।
  2. 2.कक्षा-A का औसत प्राप्तांक निश्चित रूप से बढ़ेगा ।

उपर्युक्त कथनों में से कौन-सा/कौन-से सही है/हैं ?

Read this question in English

There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.

Consider the following statements:

1. The average score of Class-B will definitely decrease.

2. The average score of Class-A will definitely increase.

Which of the above statements is/are correct?

(a) 1 only · (b) 2 only · (c) Both 1 and 2 · (d) Neither 1 nor 2

उत्तर और व्याख्या · explanation in English

Answer: (a) केवल 1

Every shifted student scored at most 21, below Class-B's lowest score of 22, so Class-B's average must fall. Class-A's average can rise or fall depending on which four students leave, so statement 2 is not certain.

  1. Each shifted student scored at most 21; every Class-B student scored at least 22.
  2. Adding scores lower than all existing scores pulls Class-B's average down — statement 1 is certain.
  3. Class-A's new average depends on whether the four who left were above or below Class-A's average.
  4. If the four scored 21 each, Class-A's average falls; if they scored 17 each, it rises — so statement 2 is not definite.
  • ✓ 1. New members all score below Class-B's minimum, so its average must decrease.
  • ✗ 2. Removing students raises the average only if they were below it; the data do not say which four moved.

Remember · Adding values below every existing value lowers the mean; removing values changes it only relative to the current mean.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q53

Easy

जय तथा विजय ने एक ही दुकान से एक ही प्रकार के कुछ पेन और विशेष पेंसिलें खरीदने के लिए समान धनराशि खर्च की । यदि जय ने 3 पेन और 5 पेंसिलें खरीदीं, और विजय ने 2 पेन और 7 पेंसिलें खरीदीं, तो निम्नलिखित में से कौन-सा सही है ?

Read this question in English

Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct?

(a) A pencil costs more than a pen · (b) The price of a pencil is equal to that of a pen · (c) The price of a pen is two times the price of a pencil · (d) The price of a pen is three times the price of a pencil

उत्तर और व्याख्या · explanation in English

Answer: (c) पेन का मूल्य, पेंसिल के मूल्य से दुगुना है

Both spent the same, so 3 pens + 5 pencils cost as much as 2 pens + 7 pencils. Cancelling the common items leaves 1 pen = 2 pencils.

  1. Equal spending: 3 pens + 5 pencils = 2 pens + 7 pencils.
  2. Remove 2 pens and 5 pencils from both sides: 1 pen = 2 pencils.
  3. So a pen costs twice as much as a pencil.

Remember · With equal totals, cancel what both sides share — the leftovers must balance.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q54

X-Ray · Core #5 Easy

एक परीक्षा में P ने Q से 40 अंक अधिक प्राप्त किए । यदि Q ने P से 10% कम अंक प्राप्त किए, तो Q ने कितने अंक प्राप्त किए ?

Read this question in English

P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score?

(a) 360 · (b) 380 · (c) 400 · (d) 420

उत्तर और व्याख्या · explanation in English

Answer: (a) 360

Q's score is 10% below P's, so the 40-mark gap is 10% of P's score. P scored 400 and Q scored 360.

  1. Q scored 10% less than P, so the gap of 40 marks is 10% of P's marks.
  2. P = 40 ÷ 0.10 = 400.
  3. Q = 400 − 40 = 360.
  4. Check: 360 is 90% of 400.

Remember · 'x% less than P' means the difference is x% of P — use it to find P first.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q55

X-Ray · Core #5 Medium

एक व्यक्ति P ने अपने तीन मित्रों में से एक मित्र X से पूछा कि उसके पास कितना धन है । X ने उत्तर दिया, “यदि Y मुझे ₹ 40 देता है, तो Y के पास Z से आधा धन होगा, किंतु यदि Z मुझे ₹ 40 देता है, तो हम तीनों के पास बराबर धन होगा ।” X, Y और Z के पास कुल कितना धन है ?

Read this question in English

A person P asks one of his three friends X as to how much money he had. X replied, “If Y gives me ₹ 40, then Y will have half of as much as Z, but if Z gives me ₹ 40, then three of us will have equal amount.” What is the total amount of money that X, Y and Z have?

(a) ₹ 420 · (b) ₹ 360 · (c) ₹ 300 · (d) ₹ 270

उत्तर और व्याख्या · explanation in English

Answer: (b) ₹ 360

The second condition gives X + 40 = Y = Z − 40, and the first gives Y − 40 = Z/2. Solving, Z = 160, Y = 120 and X = 80, a total of ₹360.

  1. Let X, Y and Z have x, y and z rupees.
  2. If Z gives X ₹40, all three are equal: x + 40 = y = z − 40.
  3. If Y gives X ₹40, Y has half of Z: y − 40 = z/2.
  4. Put y = z − 40: z − 80 = z/2, so z = 160, y = 120, x = 80.
  5. Total = 80 + 120 + 160 = ₹360.
  6. Check: after Y gives ₹40, Y has 80, half of Z's 160; after Z gives ₹40, everyone has 120.

Remember · Turn 'then all will be equal' into a chain of equalities; it reduces everything to one unknown.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q58

X-Ray · Core #5 Easy

90 प्रश्न वाली एक वस्तुनिष्ठ परीक्षा में, प्रत्येक सही उत्तर के लिए 5 अंक निर्धारित किए गए हैं और प्रत्येक ग़लत उत्तर के लिए 2 अंक घटाए जाते हैं । सभी 90 प्रश्नों का उत्तर देने पर, एक विद्यार्थी को कुल 387 अंक प्राप्त हुए । ग़लत उत्तरों की संख्या कितनी है ?

Read this question in English

In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions, a student got a total of 387 marks. What is the number of incorrect responses?

(a) 9 · (b) 13 · (c) 27 · (d) 43

उत्तर और व्याख्या · explanation in English

Answer: (a) 9

Full marks would be 90 × 5 = 450, and each wrong answer costs 5 + 2 = 7 marks compared with a right one. The shortfall of 63 marks means 9 wrong answers.

  1. If all 90 were correct: 90 × 5 = 450 marks.
  2. Each wrong answer loses 5 + 2 = 7 marks compared with a correct one.
  3. Shortfall = 450 − 387 = 63, so wrong answers = 63 ÷ 7 = 9.
  4. Check: 81 × 5 − 9 × 2 = 405 − 18 = 387.

Remember · Start from full marks and divide the shortfall by (marks for a correct answer + penalty for a wrong one).

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q70

Easy

कुछ धनराशि A, B और C के बीच में p : q : r के अनुपात में वितरित की गई ।

निम्नलिखित कथनों पर विचार कीजिए :

  1. 1.यदि p, (q + r) से अधिक हो, तो A को अधिकतम अंश मिलेगा ।
  2. 2.यदि r, (p + q) से कम हो, तो C को न्यूनतम अंश मिलेगा ।

उपर्युक्त कथनों में से कौन-सा/कौन-से सही है/हैं ?

Read this question in English

An amount of money was distributed among A, B and C in the ratio p: q: r.

Consider the following statements:

1. A gets the maximum share if p is greater than (q + r).

2. C gets the minimum share if r is less than (p + q).

Which of the above statements is/are correct?

(a) 1 only · (b) 2 only · (c) Both 1 and 2 · (d) Neither 1 nor 2

उत्तर और व्याख्या · explanation in English

Answer: (a) केवल 1

If one part exceeds the other two combined, it certainly exceeds each of them, so A gets the most. But being less than the sum of the other two says nothing about being the smallest, as 1 : 3 : 2 shows.

  1. Statement 1: shares are positive, so p > q + r means p > q and p > r — A gets the maximum. Correct.
  2. Statement 2: take p : q : r = 1 : 3 : 2. Here r = 2 < p + q = 4, yet A, not C, gets the least. Incorrect.
  3. So only Statement 1 is correct.
  • ✓ 1. p > q + r forces p above both q and r.
  • ✗ 2. r < p + q can hold even when r is not the smallest, e.g. 1 : 3 : 2.

Remember · Test 'if … then' claims with a quick counterexample: 'greater than the sum' implies 'greatest', but 'less than the sum' does not imply 'least'.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q77

Easy

X ने Y से कहा, “आपके जन्म के समय मेरी आयु आपकी वर्तमान आयु की दुगुनी थी ।” यदि X की वर्तमान आयु 42 वर्ष है, तो निम्नलिखित कथनों पर विचार कीजिए :

  1. 1.8 वर्ष पहले, X की आयु, Y की आयु की पाँच गुणा थी ।
  2. 2.14 वर्ष बाद, X की आयु, Y की आयु की दुगुनी होगी ।

उपर्युक्त कथनों में से कौन-सा/कौन-से सही है/हैं ?

Read this question in English

X said to Y, “At the time of your birth I was twice as old as you are at present.” If the present age of X is 42 years, then consider the following statements:

1. 8 years ago, the age of X was five times the age of Y.

2. After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct?

(a) 1 only · (b) 2 only · (c) Both 1 and 2 · (d) Neither 1 nor 2

उत्तर और व्याख्या · explanation in English

Answer: (b) केवल 2

X's age at Y's birth is the age gap X − Y, which equals twice Y's present age; so X = 3Y and Y = 14. Eight years ago they were 34 and 6 (not five times), but in 14 years they will be 56 and 28 (exactly twice).

  1. At Y's birth X's age was X − Y, and this equals 2Y, so X = 3Y.
  2. X = 42, so Y = 14.
  3. Statement 1: 8 years ago X was 34 and Y was 6; 5 × 6 = 30, not 34. Incorrect.
  4. Statement 2: after 14 years X will be 56 and Y 28; 56 = 2 × 28. Correct.
  • ✗ 1. 34 is not five times 6.
  • ✓ 2. 56 is exactly twice 28.

Remember · 'My age at your birth' is simply the age difference, which never changes.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q78

Easy

यदि किसी वस्तु के मूल्य में 20% ह्रास होता है और फिर नए मूल्य में 25% वृद्धि होती है, तो मूल्य में नेट परिवर्तन कितना हुआ है ?

Read this question in English

If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price?

(a) 0% · (b) 5% increase · (c) 5% decrease · (d) Cannot be determined due to insufficient data

उत्तर और व्याख्या · explanation in English

Answer: (a) 0%

A 20% cut takes ₹100 to ₹80, and 25% of 80 is 20, bringing it back to ₹100. The multipliers 0.8 × 1.25 = 1, so there is no net change.

  1. Let the price be ₹100. After a 20% decrease it is ₹80.
  2. A 25% increase on ₹80 is ₹20, giving ₹100.
  3. Net change = 0%.
  4. Check: 0.8 × 1.25 = 1.

Remember · Successive changes multiply: a fall of 1/5 is exactly undone by a rise of 1/4.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q80

Medium

एक व्यक्ति किसी कार्य के 7/8 अंश को 21 दिन में पूरा करता है । यदि कार्य की मात्रा में 50% की और वृद्धि हो जाए, तो उसे उस कार्य को समाप्त करने में कितने दिन और लगेंगे ?

Read this question in English

A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50%?

(a) 24 · (b) 21 · (c) 18 · (d) 15

उत्तर और व्याख्या · explanation in English

Answer: (d) 15

He does 1/8 of the job every 3 days, so the whole job takes 24 days. When the job grows to 1.5 times its size, 5/8 of the original job remains, which takes 15 more days.

  1. 7/8 of the job in 21 days, so the whole job takes 21 ÷ 7/8 = 24 days (1/24 of the job per day).
  2. The work is increased by 50%, so the total becomes 1.5 jobs.
  3. Work left = 1.5 − 7/8 = 12/8 − 7/8 = 5/8 of the original job.
  4. Days needed = 5/8 × 24 = 15.
  5. Check: 7/8 + 15/24 = 7/8 + 5/8 = 12/8 = 1.5 jobs.

Remember · Turn work done into a daily rate first; then express the remaining work as a fraction of the original job.

Question and answer: UPSC's official GS Paper II (2021, 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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