2 trains running in opposite directions cross a stationary lady standing at a point named F in 26 seconds and 21 seconds respectively. Further, the 2 trains cross each other in 24 seconds. Determine the ratio of the speed of the 2 trains?

3:2

The correct answer is Option (3) → 3:2

Let the lengths of the two trains be $L_1$ and $L_2$, and their speeds be $S_1$ and $S_2$ respectively.

Since each train crosses a stationary lady:

$\frac{L_1}{S_1} = 26 \Rightarrow L_1 = 26 S_1$

$\frac{L_2}{S_2} = 21 \Rightarrow L_2 = 21 S_2$

When the two trains cross each other in opposite directions:

Total relative speed = $S_1 + S_2$

Total distance = $L_1 + L_2$

$\frac{L_1 + L_2}{S_1 + S_2} = 24$

Substitute values of $L_1$ and $L_2$:

$\frac{26 S_1 + 21 S_2}{S_1 + S_2} = 24$

Multiply both sides by $(S_1 + S_2)$:

$26 S_1 + 21 S_2 = 24 (S_1 + S_2)$

$26 S_1 + 21 S_2 = 24 S_1 + 24 S_2$

Rearrange:

$2 S_1 = 3 S_2$

$\frac{S_1}{S_2} = \frac{3}{2}$

Required ratio of their speeds = 3 : 2