Question

A train travelling 100 km at x km/hr, arrives at
its destination 1 hr late. What should have
been the speed (in km/hr) for it to arrive on
time?​

Answer 1

Given info : A train travelling 100 km at x km/hr, arrives at its destination 1 hr late.

To find : what should have been the speed for it to arrive on time ?

solution : let actual time taken by train to reach the destination is t.

the train travelling 100 km at x km/h arrives at its destination 1 hr late.

i.e., 100/x = t + 1

⇒100/(t + 1) = x ...(1)

if train reaches the destination on time.

then, 100/t = speed of train (let v)

⇒100/v = t ...(2)

from equations (1) and (2),

100/(100/v + 1) = x

⇒100 = 100x/v + x

⇒100 - x = 100x/v

⇒(100 - x)/100x = 1/v

⇒v = 100x/(100 - x)

Therefore the speed of train would be 100x/(100 - x)