Question

A train leaves Pune at $7.30$ a.m. and reaches Mumbai at $11.30$ a.m. Another train leaves Mumbai at $9.30$ a.m. and reaches Pune at $1.00$ p.m. Assuming that the two trains level at constant speeds, at what time do the trains cross each other?

• A. $10.20$ a.m.
• B. $10.26$ a.m.
• C. $11.30$ a.m.
• D. Data not sufficient.

Answer 1

Answer: (B)

$10.26$ a.m.

Let the total distance between Mumbai and Pune be $D$.

Also, we assume that the trains cross each other at a time given by $x$.

Speed of train which leaves Pune is given by $\frac{D}{4}$ and that which leaves Mumbai is given by $\frac{D}{3.5}$

$(x-7.30am)\times \frac{D}{4}+(x-9.30am)\times \frac{D}{3.5}=D$

Let $x-9.30am$ be $y$

$\therefore x-7.30am=y+2$

$\Rightarrow \frac{2(y+2)}{8}+\frac{2y}{7}=1$

$\Rightarrow 14y+28+16y=56$

$\therefore y=\frac{28}{30}$ hours $=56$ minutes

$\therefore x=10.26am$