Question

Places $P_1$ and $P_2$ are $250$ km apart from each other on a national highway. A car starts from $P_1$ and another from $P_2$ at the same time. If they go in the same direction then they meet in $5$ hours and if they go in opposite directions they meet in $\frac{25}{13}$ hours. The speed of the cars are __________.

• A. $90$ km/hr, $40$ km/hr
• B. $40$ km/hr, $80$ km/hr
• C. $20$ km/hr, $60$ km/hr
• D. $50$ km/hr, $12$ km/hr

Answer 1

The correct option is A $90$ km/hr, $40$ km/hr

We know that, $s=\frac{d}{t}$ where $s=$ speed, $d=$ distance travelled and $t=$ time.

Let speed of cars be $x$ and $y$

When cars are moving in same direction,

$x-y=\frac{250}{50}=50$

When cars are moving in opposite direction,

$x+y=\frac{250\times 13}{25}=130$

Adding both the equations, we get $x-y+x+y=180$ or $x=90$ km/hr

Substituting $x$, we get $y=40$ km/hr