Time Distance

A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?

  1. 24 km
  2. 25 km
  3. 20 km
  4. 22.5 km

Solution

As B is walking fast, he reached point Y earlier. He turns back and meets A. Total distance traveled by A and B is different, but time is same.

Time = Distance/Speed

Let the distance from X to Z be a

Total distance traveled by A = a at speed of 5 km/hr

Total distance traveled by B = 27 + (27 - a) = (54 - a) at speed of 7 km/hr

Total time taken by A = a/5

Time taken by B = (54 - a)/7

Since, they have met at the same time, they would have traveled for the same time.

a/5 = (54 - a)/7

7a = 5*(54 - a) = 270 - 5a

a = 22.5 km

The correct option is D.