Question

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

Answer 1

X	Y	Total
1.5	1	2.5
1.5	1.25	2.75
1.5	1.5	3
1.5	1.75	3.25
1.5	2	3.5
7.5	7.5	15

Sorry, this was first attempt at inserting a table...

In five hours, X walks 7.5km, and Y walks 7.5km, so they take 5 hours to meet and they meet midway as they both walked 7.5km.  Therefore the correct answer is:

(c) Both 1 and 2

Answer 2

Correct option is (c) Both 1 and 2

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.