# 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 : **

## Meeting Points Analysis – X and Y

Distance between places A and B = 15 km

Speed of X = 1.5 km/hr

So, Distance covered by X in 5 hours = 7.5 km

Speed of Y in 1st hour = 1 km/hr

So, Distance covered by Y in 1st hour = 1 km

Similarly, Distance covered by Y in 2nd hour = 1.25 km

Distance covered by Y in 3rd hour = 1.5 km

Distance covered by Y in 4th hour = 1.75 km

Distance covered by Y in 5th hour = 2 km

So, the total distance covered by Y in 5 hours = 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km

**Hence, both the given statements are true.**