Question

Two men Ram and Shyam start walking simultaneously from X to Y, a distance of 84 kms, at the speeds of 5 km and 7 km an hour respectively. Shyam reaches Y, returns immediately and meets Ram at Z. Find the distance from Y to Z.

1. 14 kms
2. 18 kms.
3. 21 kms.
4. 16 kms

Answer 1

Correct Answer - Option 1 : 14 kms

Given

Distance X and Y is = 84 kms 

Let Ram and Shyam meet after time = t hours

Distance covered by Ram in t hours = 5 t km

Distance covered by Shyam in t hours = 7 t km

Relative speed 

Total distance covered by Ram and Shyam = (5t + 7t) km = 12 t km

The total distance covered by Ram and Shyam is equal to twice the distance between X and Y.

Calculation

12t = 2× 84

∴  t = 14

Total distance covered by Ram is = 14× 5 

= 70 kms

Distance between YZ = 84−70

∴ Y to Z is = 14 kms