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 ✓ UPSC's answer
- (d) Neither 1 nor 2
Why the answer is (c)
• X walks at a constant speed of 1.5 km/hr, so in 5 hours, X covers 1.5 × 5 = 7.5 km.
• Y's speed increases by 0.25 km/hr every hour: 1.0 km/hr (1st hr), 1.25 km/hr (2nd hr), 1.5 km/hr (3rd hr), 1.75 km/hr (4th hr), and 2.0 km/hr (5th hr).
• Total distance covered by Y in 5 hours is 1.0 + 1.25 + 1.5 + 1.75 + 2.0 = 7.5 km.
• Combined distance covered by X and Y in 5 hours is 7.5 + 7.5 = 15 km, which equals the total separation, so they meet exactly at 5 hours.
• Since both have covered 7.5 km each, they meet at the midpoint of the 15 km distance.
• Therefore, both statements 1 and 2 are correct, making option (c) the right answer.
Why the other options are wrong
- (a) 1 only
- Statement 2 is also correct because both X and Y cover exactly 7.5 km each, meeting at the midpoint.
- (b) 2 only
- Statement 1 is also correct because the sum of distances covered by X and Y reaches 15 km exactly at the end of the 5th hour.
- (d) Neither 1 nor 2
- Both statements are factually correct based on the calculated distances and meeting time.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.