Question

The speeds of two trains A and B are in the ratio of 5:6. A takes 36 minutes more than B to reach a destination. What is the time taken by A to reach the destination to cover the same distance?

Answer 1

Let the distance be 'l'. Now the velocities of A, B are 5v, 6v. Time taken to cover distance l is t(A)=l/(5v) and t(B)=l/(6v). Given that A takes 36 minutes more than B i.e. tA-tB=36. Which is l/v[1/5-1/6]=36, l/(5*6*v)=36. Hence l/(5v)=36(6). Therefore, time taken by A is 216 minutes.

Answer 2

Let the common factor be x
Speed of A= 5x & Speed of B= 6x
Let the distance be= d
ATQ
$\frac{d}{5x}$=$\frac{d}{6x}$+36
⇒ d=1080x
Time taken by A to travel distance d= $\frac{d}{5x}$
                                                     =1080x÷5x
                                                     =216