Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
2 : 5
Train Speed Ratio Calculation
Let the speed of the first train be $s_1$ and its length be $l_1$. Let the speed of the second train be $s_2$ and its length be $l_2$.
Train Crossing Man
- When a train crosses a stationary man, the distance covered equals the train's length.
- Train 1 crosses a man in 25 seconds. So, $l_1 = s_1 \times 25$.
- Train 2 crosses a man in 32 seconds. So, $l_2 = s_2 \times 32$.
Trains Crossing Each Other
- When two trains move in opposite directions, their relative speed is the sum of their speeds ($s_1 + s_2$).
- The total distance covered when they cross each other is the sum of their lengths ($l_1 + l_2$).
- They cross each other in 30 seconds. So, $l_1 + l_2 = (s_1 + s_2) \times 30$.
Calculating the Speed Ratio
Substitute the expressions for $l_1$ and $l_2$ into the equation for crossing each other:
$ (s_1 \times 25) + (s_2 \times 32) = (s_1 + s_2) \times 30 $
Now, simplify the equation:
$ 25s_1 + 32s_2 = 30s_1 + 30s_2 $
Rearrange the terms to find the ratio:
$ 32s_2 - 30s_2 = 30s_1 - 25s_1 $
$ 2s_2 = 5s_1 $
Express this as a ratio:
$ \frac{s_1}{s_2} = \frac{2}{5} $
The ratio of their speeds ($s_1 : s_2$) is 2 : 5.
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