Question

Train A leaves Mumbai for Pune at $5:30$ a.m. and reaches Pune at $9:30$ a.m. Train B leaves Pune for Mumbai at $7:30$ a.m. and reaches Mumbai at $13:30$ hrs. At what time will these two trains meet?

• A. $9:30$ a.m.
• B. $9:42$ a.m.
• C. $8:42$ a.m.
• D. None of these

Answer 1

The correct option is C $8:42$ a.m.

Train $A$ takes $4hrs$ to complete its journey

and train $B$ takes $6hrs$ to complete its journey.

Let the total journey $=D$.

Speed of train $A=\frac{D}{4}$

and speed of train $B=\frac{D}{6}$.

Distance covered by train $A$ in $2hrs=\frac{D}{4}\times 2=\frac{D}{2}$.

$\therefore$ Remaining distance $=\frac{\frac{D}{2}}{\frac{D}{4}+\frac{D}{6}}$

$=\frac{\frac{D}{2}}{\frac{6D+4D}{24}}$

$=\frac{\frac{D}{2}}{\frac{10D}{24}}$

$=\frac{D}{2}\times \frac{24}{10D}$

$=\frac{6}{5}hrs=1hr12min$.

$\therefore$ Trains will meet at $7.30+1hr12min.=8.42A.M.$