Question

If a train takes $1.5$ seconds to cross a telegraph post and $1.75$ seconds to overtake a cyclist racing along a road parallel to the track at $10$ m/s, then the length of the train is

• A. $135$ meters
• B. $125$ meters
• C. $115$ meters
• D. $105$ meters

Answer 1

The correct option is D $105$ meters

Let the length of train be $l$ metres and its speed be $x$ m/s
Then $\frac{l}{x}=1.5$

$\Rightarrow l=1.5x$ ............(i)
and $\frac{l}{(x-10)}=1.75$

$\Rightarrow l=1.75x(x-10)$
$\Rightarrow l=1.75x-17.5$ ..............(ii)
From (i) and (ii), we have
$1.5x=1.75x-17.5$

$\Rightarrow$ $0.25x=17.5$

$\Rightarrow$ $x=\frac{17.5}{0.25}=70$ m/s
$\therefore$ Length of the train $=(1.5\times 70)$ metres $=105$ metres .