Question

Two trains start simultaneously from two stations $300$ km apart and move towards each other.The speed of one train is more than the other by $20$ km/hr. If the distance between the trains after two hours is $20$ km, find the speeds of the trains.

• A. Speed of the first train is $40$ km/hr and Speed of the second train is $60$ km/hr
• B. Speed of the first train is $60$ km/hr and Speed of the second train is $80$ km/hr
• C. Speed of the first train is $100$ km/hr and Speed of the second train is $80$ km/hr
• D. Speed of the first train is $70$ km/hr and Speed of the second train is $90$ km/hr

Answer 1

The correct option is B Speed of the first train is $60$ km/hr and Speed of the second train is $80$ km/hr

Let the trains start from station $A$ and station $B$ respectively.

Let the first train start from station $A$ and the second train start from station $B$ at the same time and move towards each other.
Let the speed of the first train be $x$ km/hr
$\therefore$ the speed of the second train $=(x+20)$ km/hr
Distance travelled by first train in $2$ hours $=2x$ km
Distance travelled by second train in $2$ hours $=2(x+20)$ km $=(2x+40)$ km
Given, distance between two stations $=300$ km
According to the given condition, we have
Distance travelled by first train $+$ Distance travelled by second train $+20=300$
i.e., $2x+(2x+40)+20=300$
$4x+60=300$
$4x=300-60$ ....[Transposing $60$ to RHS]
$4x=240$
Thus, $x=$ $\frac{240}{4}$ $=60$
$\therefore$ Speed of the first train $=60$ km/hr and
speed of the second train $=(60+20)$ krn/h $=80$ km/hr.