Arithmetic: percentage, ratio, averages, time & work

Answer: (c) 3: 4

Distance is the area under a velocity–time graph. A's distance is the triangle OLP and B's is the rectangle of height LD over OL; since PL = 3/2 × LD, the triangle is 3/4 of the rectangle.

1. Let LD (B's constant velocity) = 2 units; then PD = 1 and A's velocity at time L is PL = PD + DL = 3.
2. Distance of B in time OL = rectangle = OL × 2 = 2 × OL.
3. Distance of A in time OL = triangle OLP = 1/2 × OL × 3 = 1.5 × OL.
4. Ratio A : B = 1.5 : 2 = 3 : 4.

Remember · On a velocity–time graph, distance = area under the line: a triangle for steady acceleration from rest, a rectangle for constant speed.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 1 Oct 2026 (how we verify). Permalink · Report an error

Answer: (d) 18

To pass a man standing still, the train covers only its own length, 200 m. At 40 km/h, which is 100/9 m/s, that takes 18 seconds.

1. Distance to cover = length of the train = 200 m (the man adds no length).
2. Speed: 40 km/h = 40 × 5/18 = 100/9 m/s.
3. Time = 200 ÷ (100/9) = 18 seconds.
4. Check: in 18 s at 40 km/h the train covers 40,000 × 18 ÷ 3600 = 200 m.

Remember · A train passing a pole or a standing person covers only its own length; convert km/h to m/s by multiplying by 5/18.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) 3ax + 8

Total sale = ax + (a + 2)(x + 2) + (a − 2)(x − 2). The terms 2a + 2x and −2a − 2x cancel, leaving 3ax + 8.

1. Geography: a × x = ax.
2. History: (a + 2)(x + 2) = ax + 2a + 2x + 4.
3. Mathematics: (a − 2)(x − 2) = ax − 2a − 2x + 4.
4. Sum: 3ax + 8.
5. Check with a = 3, x = 5: 15 + 5 × 7 + 1 × 3 = 53, and 3 × 3 × 5 + 8 = 53.

Remember · Check algebraic options by putting small numbers into both the question and each option.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (a) 6: 5

A covers half the track, 180°. B started 30° ahead and is caught at that same point, so B covered 180° − 30° = 150° in the same time. The speeds are in the ratio 180 : 150 = 6 : 5.

1. A runs from his start to the diametrically opposite point: an arc of 180°.
2. B started 30° ahead in the direction of running and is met there: B runs 180° − 30° = 150°.
3. Same time, so speed ratio = arc ratio = 180 : 150 = 6 : 5.

Remember · On a circular track, measure distances as angles; in equal time, the speed ratio equals the ratio of arcs covered.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) 150

Scoring 30 and falling 30 short means the pass mark is 60. If 60 is 40% of the maximum, the maximum is 60 ÷ 0.4 = 150.

1. Pass mark = marks scored + shortfall = 30 + 30 = 60.
2. 40% of maximum = 60, so maximum = 60 × 100 ÷ 40 = 150.
3. Check: 40% of 150 = 60, and 60 − 30 = 30.

Remember · Pass mark = marks scored + shortfall; divide it by the pass percentage to get the maximum marks.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) ₹30

An equal percentage profit and loss on the same cost means the two selling prices lie equally far above and below the cost. The cost is the average of ₹40 and ₹20, i.e. ₹30 (profit and loss both 33⅓%).

1. Let the cost be C. Then 40 = C(1 + X/100) and 20 = C(1 − X/100).
2. Adding the two: 60 = 2C, so C = ₹30.
3. Check: ₹40 is 33⅓% above ₹30, and ₹20 is 33⅓% below it.

Remember · Same percentage profit and loss on one cost price: the cost is the average of the two selling prices.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) 10

18 adults take the same space as 30 children, so one adult equals 5/3 of a child. 12 adults use the space of 20 children, leaving room for 10.

1. 18 adults = 30 children, so 1 adult = 30/18 = 5/3 children.
2. 12 adults = 12 × 5/3 = 20 children's worth of space.
3. Room left = 30 − 20 = 10 children.
4. Check: 12 adults fill 12/18 = 2/3 of the lift; the remaining 1/3 of 30 children is 10.

Remember · Convert everything to one unit (here child-spaces), subtract what is used, and read off what remains.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) ₹11,250

Add a year's interest (12.5%, one-eighth) to the balance and subtract each payment. The balance falls to ₹17,000 after year 1 and ₹10,000 after year 2, so year 3 needs ₹10,000 × 1.125 = ₹11,250.

1. Year 1: 22,800 × 1.125 = 25,650; after paying 8,650 the balance is 17,000.
2. Year 2: 17,000 × 1.125 = 19,125; after paying 9,125 the balance is 10,000.
3. Year 3: 10,000 × 1.125 = 11,250 clears the debt.
4. Check: ₹10,000 is only the balance at the start of year 3; it still earns a year's interest.

Remember · For instalments at compound interest, roll the balance forward: add the year's interest, subtract the payment. 12.5% is one-eighth.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error