Question

A train running at a uniform speed passes a bridge $275$ m long in $15$ seconds and another bridge $425$ m long in $21$ seconds. Find the length of the train.

• A. $120$ m
• B. $130$ m
• C. $100$ m
• D. $80$ m

Answer 1

Answer: (C)

$100$ m

Let the speed of the train be $s$ m\sec
and length of train be $L$ m.
Given Equation:

Bridge of distance $275$ m and time is $15$ seconds.
Bridge of distance $425$ m and time is $21$ seconds.
Factor to consider is length of train.
Hence total length $=$ Bridge length $+$ Length of train
According to the formula:
Speed $=\frac{Distance}{Time}$
Equation 1: $s=\frac{L+275}{15}$
Similarly for equation 2: $s=\frac{L+425}{21}$
From Equation 1 and Equation 2.
$\frac{L+275}{15}=\frac{L+425}{21}$
$\Rightarrow 21\times \left(L+275\right)=15\times \left(L+425\right)$
$\Rightarrow 21\times L+21\times 275=15\times L+15\times 425$
$\Rightarrow 6\times L=600$
$\Rightarrow L=100$ m