Question : A train crosses a stationary pole completely in 18 seconds and a bridge completely in 44 seconds. If the length of the bridge is 650 meters, then what is the length of the train?
Option 1: 540 m
Option 2: 360 m
Option 3: 450 m
Option 4: 270 m
Correct Answer: 450 m
Solution :
Let the length of the train be $l$ and the speed of the train be $s$.
Time = 18 sec
So, $s = \frac{l}{18}$ --------(i)
Length of the bridge = 650 m
Total distance = $650+l$
Time = 44 sec
$s = \frac{650+l}{44}$ --------(ii)
from (i) and (ii)
$\frac{l}{18} = \frac{650+l}{44}$
⇒ $44l = 18(650+l)$
⇒ $44l = 18l + 11700$
⇒ $26l = 11700$
⇒ $l = \frac{11700}{26}$
= 450 m
Hence, the correct answer is 450 m.
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