Q. 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
(d) Neither 1 nor 2
Correct Answer: (c) Both 1 and 2
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
A person X from place a & other Y from B
Given information:
– Total distance between A and B = 15 km
– Person X’s speed = constant 1.5 km/hr
– Person Y’s speed increases by 0.25 km/hr every hour:
Hour 1: 1.0 km/hr
Hour 2: 1.25 km/hr
Hour 3: 1.5 km/hr
Hour 4: 1.75 km/hr
Hour 5: 2.0 km/hr
Step 1: Calculate X’s distance in 5 hours
– X’s distance = Speed × Time
– X’s distance = 1.5 × 5 = 7.5 km
Step 2: Calculate Y’s total distance in 5 hours
– Hour 1: 1.0 km
– Hour 2: 1.25 km
– Hour 3: 1.5 km
– Hour 4: 1.75 km
– Hour 5: 2.0 km
Total = 7.5 km
Step 3: Verify statements
1. They take 5 hours to meet
– Total distance covered = X’s distance + Y’s distance
– 7.5 + 7.5 = 15 km (complete distance)
– Therefore, they meet in 5 hours (True)
2. They meet midway
– Both cover 7.5 km each
– 7.5 km is exactly half of 15 km
– Therefore, they meet midway (True)
Answer: Option (c) Both statements 1 and 2 are correct.
