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 ?

Answer: Option C

$$\begin{array}{rl}& \text{A}\text{:}\text{B}\text{length}\\ & \text{Ratio of A’s and }\to 5:3\left(5x:3x\right)\\ & \text{ B’s length}\\ & \text{Ratio of A’s and }\to 6:5\left(6y:5y\right)\\ & \text{ B’s speed}\end{array}$$
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 :
$$\begin{array}{rl}& =\text{A}:\text{B}\\ & =\frac{5x}{6y}:\frac{3x}{5y}\\ & =25:18\end{array}$$