Question

Train A leaves from P to Q. Half an hour later train B leaves for P from Q. Two hours after A had started, the trains meet. A has covered 50 % more distance than train B when they meet. What is the ratio of the speeds of train A to train B?

• A. $9:8$
• B. $8:9$
• C. $5:7$
• D. $8:3$

Answer 1

The correct option is A $9:8$

Let speed of $A$ is $x$ and speed of $B$ is $y$.

$\therefore$ Distance covered by $A$ in $2hrs=2x$

Given:Half an hour later train $B$ leaves for $P$ from $Q$

Distance covered by $B$ in $1.5hrs=1.5y$.

Also $2x=1.5\left(1.5y\right)$

$\Rightarrow \frac{x}{y}=\frac{2.25}{2}$

$\Rightarrow \frac{x}{y}=\frac{2.25\times 4}{2\times 4}=\frac{9}{8}$

Hence $x:y=9:8$.

The ratio of the speeds of train $A$ to train $B$ is $9:8$.