The ratio of lengths of two trains is 5 : 3 and the ratio of their speeds is 6 : 5. The ratio of time taken by them to cross a pole is ?

Solution (By Examveda Team)

$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{A}}\,{\text{:}}\,{\text{B}}\,\,\,\,\,\,\,{\text{length}} \cr & {\text{Ratio of A's and }} \to 5:3\,\,\,\left( {5x:3x} \right) \cr & {\text{ B's length}} \cr & {\text{Ratio of A's and }} \to 6:5\,\,\,\left( {6y:5y} \right) \cr & {\text{ B's speed}} \cr} $$
We know that,
When a train crosses a pole, i.e., it covers the distance equal to its length
Time taken by train A to cross the pole :
$$ = \frac{{{\text{Total distance}}}}{{{\text{Speed}}}} = \frac{{5x}}{{6y}}$$
Time taken by train B to cross the pole :
$$ = \frac{{{\text{Total distance}}}}{{{\text{Speed}}}} = \frac{{3x}}{{5y}}$$
Ratio of the their time :
$$\eqalign{ & = {\text{A}}:{\text{B}} \cr & = \frac{{5x}}{{6y}}:\frac{{3x}}{{5y}} \cr & = 25:18 \cr} $$