Question

If the speed of a train is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the train.

• A. 400 km/hr
• B. 360 km/hr
• C. 420 km/hr
• D. 380 km/hr

Answer 1

The correct option is A 400 km/hr

Let the speed of the train be $x$ km/hr.

$Time=\frac{Distance}{Speed}$

$\therefore$ Time taken to cover 1200 km = $\frac{1200}{x}$

Reduced speed = $(x-40)$ km/hr

$\therefore$ Time taken to cover 1200 km in reduced speed = $\frac{1200}{x-40}$

Relation between the time taken to cover 1200 km with speed x and with speed (x - 40) km/hr is as given below

$\frac{1200}{x-40}-\frac{1200}{x}=\frac{1}{3}$ $(\because 20minutes=\frac{1}{3}hours)$
$\Rightarrow$ $\frac{48000}{x(x-40)}=\frac{1}{3}$
$\Rightarrow$ $144000=x^2-40x$
$\Rightarrow$ $x^2-40x-144000=0$
$\Rightarrow$ $x^2-400x+360x-144000=0$
$\Rightarrow$ $x(x-400)+360(x-400)=0$
$\Rightarrow$ $(x+360)(x-400)=0$
$\Rightarrow$ $x=-360orx=400$
Since speed cannot be negative, we get x = 400 km/hr.
$\therefore$ The speed of the train is 400 km/hr.