Question

A train leaves Pune at $7: 30 \,am$ and reaches Mumbai at $11:30 \,am$. Another train leaves Mumbai at $9:30 \,am$ and reaches Pune at $1:00\,pm$. 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 $x \,km$.
Time taken by $1 ^\text{st}$ train $=4 \,h$
$\therefore$ 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 $=\frac{x}{(7 / 2)}=\frac{2 x}{7} km / h$
1st train starts from $7: 30$ am and $2^\text{nd}$ train starts from $9: 30 \,am$.
Distance travelled by $1^\text{ st}$ train in $2\, h$
$=\frac{x}{2} \,km$
Let they meet at time $t$.
$\therefore \frac{x}{2}=\left(\frac{x}{4} \times t\right)+\left(\frac{2 x}{7}\right) t$
$\Rightarrow t=\left(\frac{14}{15}\right) h$
$\Rightarrow t=\left(\frac{14}{15} \times 60\right) \min =56 \min$
$\therefore$ They meet at $9: 30+56=10: 26$ am