Let the height of the mountain

* *be

* d* km.

Let

*x* km/hr be the speed of Rakesh (while climbing up) and

*y* km/hr be the speed of Rajesh.

∴ We can write,

*x* = 7

*k* and

*y* = 8

*k* where '

*k*' is a natural number

They both meet each other when Rakesh is moving down and Rajesh is climbing up.

Let they both meet each other at height

*h* from the ground level and let after

*t* hr from the time when they meet, both return to the starting point.

∴ For Rakesh,

*h* = 7

*k* × 4/5 ×

*t* ...(i)

and for Rajesh, (

*d* −

*h*) +

*d* = 8

*k* ×

*t* ...(ii)

On solving equations (i) and (ii), we get,

*h* = (14/17)

*d*Hence, option 5.