Arithmetic: percentage, ratio, averages, time & work

Answer: (d) 64/729th part of the population

Each year one-third leaves, so two-thirds of the previous year's population remains. The fraction compounds, so after six years the population left is (2/3)⁶ = 64/729 of the original.

1. After one year, 1 − 1/3 = 2/3 of the population remains.
2. The same fraction applies to what is left each year, so after 6 years the remainder is (2/3)⁶.
3. (2/3)⁶ = 2⁶/3⁶ = 64/729.
4. Check: the denominator must be 3⁶ = 729 and the numerator 2⁶ = 64; only (d) has both.

Remember · Repeated fractional loss compounds: after n rounds of losing 1/k, the remainder is (1 − 1/k)ⁿ, not 1 − n/k.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) 163 cm

A spider does not slip back in the chance in which it reaches the top, so height = 39 net gains + one full climb. That gives X = 201 cm, Y = 163 cm and Z = 182 cm; the shortest pillar is 163 cm.

1. Net gain per chance: A = 6 − 1 = 5 cm, B = 7 − 3 = 4 cm, C = 6.5 − 2 = 4.5 cm.
2. In the 40th chance each spider reaches the top and does not slip, so height = 39 × (net gain) + (full climb).
3. X = 39 × 5 + 6 = 201 cm; Y = 39 × 4 + 7 = 163 cm; Z = 39 × 4.5 + 6.5 = 182 cm.
4. Shortest pillar = 163 cm (Y).
5. Check for Y: after 38 chances B is at 152 cm and reaches only 159 cm in the 39th climb, so it truly needs the 40th.

Remember · Climb-and-slip problems: the last climb has no slip. Height = (n − 1) × net gain + one full climb.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) Gain 1%

Take Gopal's cost as ₹100. Ram pays ₹110 and offers the phone back at 10% less, ₹99 — ₹1 below what Gopal first paid, a 1% gain. UPSC's options compare this buy-back price with Gopal's original cost.

1. Let Gopal's cost be ₹100.
2. Sold to Ram at 10% profit: ₹110.
3. Ram sells it back at 10% loss on his cost: 110 × 0.9 = ₹99.
4. Gopal gets back for ₹99 the phone that first cost him ₹100: a gain of ₹1 on ₹100 = 1%.
5. Note: counting both deals, Gopal ends ₹11 ahead (+110 − 99); no option matches that, so the options measure only the buy-back price against his original cost.

Remember · A rise of x% then a fall of x% leaves the price x²/100 % below the start: 10% up, 10% down → 1% lower.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) 50 kg

The first five and the last five together cover all nine persons, with the 5th person counted twice. So the 5th person's weight = (5 × 45 + 5 × 55) − 9 × 50 = 500 − 450 = 50 kg.

1. Total of 9 persons = 9 × 50 = 450 kg.
2. First 5 = 5 × 45 = 225 kg; last 5 = 5 × 55 = 275 kg.
3. 225 + 275 = 500 kg, which counts the 5th person twice.
4. 5th person = 500 − 450 = 50 kg.

Remember · When two overlapping groups together cover everyone, (sum of the groups) − (grand total) = the overlap.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) None of the above can be concluded with certainty.

P − Q = 0.15B − 0.10A, and its sign depends on how much bigger A is than B. If A is less than 1.5 times B, P is larger; if more, Q is larger; at exactly 1.5 times they are equal. So nothing can be concluded.

1. P − Q = (0.40A + 0.65B) − (0.50A + 0.50B) = 0.15B − 0.10A.
2. P > Q when 0.15B > 0.10A, i.e. A < 1.5B; Q > P when A > 1.5B; P = Q when A = 1.5B.
3. A > B allows all three: A = 1.2, B = 1 gives P > Q; A = 3, B = 1 gives Q > P; A = 1.5, B = 1 gives P = Q.
4. So the comparison cannot be fixed.

Remember · Subtract the two expressions and study the sign; if it depends on a ratio the question does not fix, the answer is 'cannot be determined'.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) 240

The 22% earning above ₹1,00,000 includes the 6% above ₹2,00,000, so 16% earn between ₹1,00,000 and ₹2,00,000. The 990 households between ₹30,000 and ₹1,00,000 are the remaining 66%, which makes 1500 households in all; 16% of 1500 = 240.

1. Above ₹1,00,000: 22%. Below ₹30,000: 12%. So ₹30,000–₹1,00,000: 100 − 22 − 12 = 66%.
2. 66% = 990 households, so the total = 990 ÷ 0.66 = 1500.
3. ₹1,00,000–₹2,00,000: 22% − 6% = 16% (the 22% already includes the 6% above ₹2,00,000).
4. 16% of 1500 = 240.

Remember · 'More than X' groups are cumulative; subtract the higher band to get the slab in between before converting to numbers.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (a) 25%

Take the one-third portion as 1 litre: it holds 0.5 litre of water. Adding 1 litre of pure milk makes 2 litres with the same 0.5 litre of water, which is 25%.

1. Let the portion taken (1/3rd of the sample) be 1 litre; at 50% water it has 0.5 litre of water.
2. Add an equal amount (1 litre) of pure milk, which has no water: total 2 litres.
3. Water = 0.5 ÷ 2 = 25%.

Remember · Adding an equal amount of the pure component halves the concentration; the size of the portion taken does not matter.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) 240 km

The freight train has an 80 km lead when the express starts. The express closes the gap at 20 km/h, taking 4 hours, by which time it has run 60 × 4 = 240 km from Delhi.

1. Lead of the freight train when the express starts = 40 × 2 = 80 km.
2. Relative speed = 60 − 40 = 20 km/h, so time to catch up = 80 ÷ 20 = 4 h.
3. Distance of the express from Delhi = 60 × 4 = 240 km.
4. Check: the freight train has run 40 × 6 = 240 km in 6 hours.

Remember · Catch-up time = head start ÷ relative speed; then distance = the chaser's speed × that time.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (a) 3: 1: 1

Working together for the same time, each person's share of the earnings follows his rate of work. With P = 3Q and P + Q = 4R, we get 4Q = 4R, so R = Q and the ratio is 3 : 1 : 1.

1. Let Q's rate be 1 unit a day; then P's rate = 3.
2. P + Q = 4 = 4 × R's rate, so R's rate = 1.
3. Working for the same time, their shares follow their rates: P : Q : R = 3 : 1 : 1.

Remember · When people work together for the same time, split the earnings in the ratio of their work rates.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) 0.80 inch

The six days total 6 × 0.50 = 3.00 inches and the first four days 4 × 0.40 = 1.60 inches, so the last two days had 1.40 inches. Split in the ratio 4 : 3, the fifth day had 1.40 × 4/7 = 0.80 inch.

1. Total for six days = 6 × 0.50 = 3.00 inches.
2. Total for the first four days = 4 × 0.40 = 1.60 inches.
3. Last two days = 3.00 − 1.60 = 1.40 inches.
4. Fifth day : sixth day = 4 : 3, so the fifth day = 1.40 × 4/7 = 0.80 inch.
5. Check: sixth day = 0.60 inch, and 1.60 + 0.80 + 0.60 = 3.00.

Remember · Turn averages into totals first, then split the remaining total in the given ratio.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) ₹ 42,000

Let incomes be 4k and 3k and expenses 3m and 2m. Equal savings give 4k − 3m = 3k − 2m, so k = m, and then 4k − 3k = ₹6,000 gives k = ₹6,000. Total income = 7k = ₹42,000.

1. Incomes: 4k and 3k; expenses: 3m and 2m.
2. Savings: 4k − 3m = 6000 and 3k − 2m = 6000.
3. Subtracting: k − m = 0, so m = k. Then 4k − 3k = k = 6000.
4. Total income = 4k + 3k = 7 × 6000 = ₹42,000.
5. Check: X earns ₹24,000 and spends ₹18,000; Y earns ₹18,000 and spends ₹12,000 — each saves ₹6,000.

Remember · When both save the same amount, equate the two savings expressions first — it links the two ratio multipliers.

Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error