Question

Two cars start towards each other, from two places $A$ and $B$ which are at a distance of $160$ km. The start at the same time $8:10$ AM. If the speeds of the cars are $50$ km and $30$ km per hour respectively, they will meet each other at

• A. $10:10$ AM
• B. $10:30$ AM
• C. $11:10$ AM
• D. $11:20$ AM

Answer 1

The correct option is A $10:10$ AM

$A$--------------------$X$ km--------------$P$--------------$(160-X)$ km-----------------$B$
Speed of $B=30$ kmph
Let time taken to meet at point $P$ is same as both train started at same time .
Now,
Time taken to traveled $X$ km by $A=\frac{X}{50}$ .........(i)
Time taken to traveled $(160-X)$ km by $B=\frac{(160-X)}{30}$ ............(ii)
Comparing equation (i) and (ii), we have
$\frac{X}{50}=\frac{(160-X)}{30}$
$\Rightarrow 3X=800-5X$
$\Rightarrow 8X=800$
$\Rightarrow X=100$ km
Time taken by $A$ to traveled $100=\frac{100}{50}=2$ hours.
So, they will at $10:10$ AM.