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:

Method 1: Very simple question and can be solved without pen and paper. Just assume both statements to be true and check their validity.

Distance between places A and B = 15 km and they meet midway so each covers 7.5 km distance.
Speed of X = 1.5 km/hr, so time taken = 7.5/1.5 = 5 hrs

Check if B can successfully cover 7.5 km in 5 hours. If yes, we have validated both statements by reverse logic.

Average speed of B = Mid value of 5 speeds with equal time slots – 1, 1.25, 1.5, 1.75, 2 = 1.5 km/hr

Method 2: 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.