KVPY SA Exam 2012 Question Paper

First train from Pune to Mumbai takes 4hrs.
Second train from Mumbai to Pune takes 3.5hrs.
Speed of train from Pune to Mumbai is ${\mathrm{V}}_1=\frac{\mathit{d}}{4}$
Speed of train from Mumbai to Pune is ${\mathrm{V}}_2=\frac{\mathit{d}}{3.5}$
Distance traveled by first train till 9:30 is $\mathit{x}=\frac{\mathit{d}}{4}\times 2=\frac{\mathit{d}}{2}$
Say now both trains meet after time from 9:30
$\frac{\mathit{x}}{\mathit{d}∕4}=\frac{\frac{\mathit{d}}{2}-\mathit{x}}{\frac{\mathit{d}}{3.5}}$
$\Rightarrow \frac{4\mathit{x}}{\mathit{d}}=\frac{3.5}{2}-\frac{3.5\mathit{x}}{\mathit{d}}$
$\Rightarrow \frac{7.5\mathit{x}}{\mathit{d}}=\frac{3.5}{2}$
$\Rightarrow 15\mathit{x}=3.5\mathit{d}\Rightarrow 30\mathit{x}=7\mathit{d}$
time taken by first train from 9: 30 is $\frac{4\mathit{x}}{\mathit{d}}=4\left(\frac{7}{30}\right)$ $=\frac{14}{15}$ = 56 min
Then both train meet at 9.30 + 56 min = 10 : 26 am