Question

A train leaves Pune at $7:30am$ and reaches Mumbai at $11:30am$. Another train leaves Mumbai at $9:30am$ and reaches Pune at $1:00pm$. Assuming that the two trains travel at constant speeds, at what time do the two trains cross each other?

• A. $10:20$ am
• B. $11:30$ am
• C. $10:26$ am
• D. data not sufficient

Answer 1

Answer: (C)

Let the distance between Pune and Mumbai be $xkm$.
Time taken by $1^{\text{st}}$ train $=4h$
$\therefore$ Speed of $1^{\text{st}}$ train $=\frac{x}{4}km/h$
Time taken by $2^{\text{nd}}$ train $=\frac{7}{2}h$
$\therefore$ Speed of $2^{\text{nd}}$ train $=\frac{x}{(7/2)}=\frac{2x}{7}km/h$
1st train starts from $7:30$ am and $2^{\text{nd}}$ train starts from $9:30am$.
Distance travelled by $1^{\text{ st}}$ train in $2h$
$=\frac{x}{2}km$
Let they meet at time $t$.
$\therefore \frac{x}{2}=\left(\frac{x}{4}\times t\right)+\left(\frac{2x}{7}\right)t$
$\Rightarrow t=\left(\frac{14}{15}\right)h$
$\Rightarrow t=\left(\frac{14}{15}\times 60\right)\min =56\min$
$\therefore$ They meet at $9:30+56=10:26$ am