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:
Answer & explanation
Answer: (c) Both 1 and 2
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.
- Distance closed in each hour: 1.5 + 1 = 2.5, then 1.5 + 1.25 = 2.75, then 3, 3.25, 3.5 km.
- Running total: 2.5, 5.25, 8.25, 11.5, 15 km — they meet at the end of the 5th hour.
- X covers 5 × 1.5 = 7.5 km; Y covers 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km.
- Each covers half of 15 km, so they meet midway.
- 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). ·