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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 2023 · Q20

Medium

A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements:

  1. 1.The work will be finished on Thursday.
  2. 2.The work will be finished in 10 days.

Which of the above statements is/are correct?

Answer & explanation

Answer: (a) 1 only

Take the work as 48 units: A does 6, B 3 and C 4 units a day, so each 3-day round finishes 13 units. After 9 days 39 units are done; A adds 6 on day 10 and B completes the last 3 on day 11. Counting from Monday, day 11 is a Thursday.

  1. Total work = LCM(8, 16, 12) = 48 units. A does 6, B does 3 and C does 4 units a day.
  2. One round (A, B, C) = 6 + 3 + 4 = 13 units in 3 days. After 3 rounds (9 days): 39 units, so 9 units remain.
  3. Day 10 (A): 39 + 6 = 45 units. Day 11 (B): 45 + 3 = 48 units — the work is complete.
  4. Day 1 is Monday, so day 8 is Monday again and day 11 is Thursday.
  5. Statement 1 is correct; statement 2 is not, because the work takes 11 days.
  • ✓ 1. The work ends on day 11, and day 11 counted from a Monday is a Thursday.
  • ✗ 2. After 10 days only 45 of the 48 units are done; B needs day 11 to finish.

Remember · Take the LCM of days as total work, add round by round, then day by day; convert day numbers to weekdays using remainders by 7.

Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2023 · Q44

Easy

A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct?

Answer & explanation

Answer: (c) R < S

At the same rate, half-yearly compounding earns interest on interest and so grows faster than annual compounding. To reach the same amount Q in one year, the half-yearly rate R must therefore be smaller than the annual rate S.

  1. Half-yearly at R% a year: Q = P(1 + R/200)². Annually at S%: Q = P(1 + S/100).
  2. So 1 + S/100 = (1 + R/200)² = 1 + R/100 + R²/40000.
  3. S = R + R²/400, which is greater than R for any positive rate.
  4. Example: R = 10 gives (1.05)² = 1.1025, so S = 10.25. Hence R < S.
  5. Option (d), R ≤ S, is not false as a statement, but equality never occurs for a positive rate; the exact relation is R < S.

Remember · More frequent compounding at the same rate gives more; to give the same amount, the more frequent rate must be lower.

Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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