Question

It takes eight hours for a $600$ km journey, if $120km$ is done by train and the rest by car. It takes $20$ minutes more, if $200km$ is done by train and the rest by car. The ratio of the speed of the train to that of the car is

• A. $3:5$
• B. $3:4$
• C. $4:3$
• D. $4:5$

Answer 1

Answer: (B)

$3:4$

Let speed of train by $xkm/hr$ and speed of car be $ykm/hr$.
According to the question,
$\frac{120}{x}+\frac{480}{y}=480.....\left(1\right)$
$\frac{200}{x}+\frac{400}{y}=500....\left(2\right)$
Dividing $\left(1\right)$ by $\left(2\right)$,
$\frac{120(\frac{1}{x}+\frac{4}{y})=480}{100(\frac{2}{x}+\frac{4}{y})=500}\Rightarrow \frac{y+4x}{2y+4x}=\frac{4}{5}$
$5y+20x=8y+16x$
$4x=3y$
$\frac{x}{y}=\frac{3}{4}$
$\frac{\text{Speed of train}}{\text{Speed of car}}=\frac{3}{4}$.