1)

A man standing on a 170 m long platform watches that a train takes  $7\frac{1}{2}$ seconds to pass him and 21 seconds to cross the platform. Find the length of the train and its speed.

A) $94\frac{4}{9}$ , $12\frac{16}{27}$

B) $92\frac{4}{9}$ , $12\frac{16}{27}$

C) $94\frac{4}{3}$ , $14\frac{16}{9}$

D) $94\frac{4}{3}$ , $14\frac{15}{9}$

E) None of these

Option A

### Explanation:

Let the length of the train be $x$ m and its speed $y$ m/sec.

Distance covered in crossing the platform $=170+x$ m

Time taken = 21 seconds

Speed $y=\frac{(170+x)}{21}$ -----------------(1)

Distance covered in crossing the man $=x$ mts

Time Taken $=7\frac{1}{2}$ $=\frac{15}{2}$ sec

Speed $y=\frac{x}{\frac{15}{2}}$ $=\frac{2x}{15}$ ------------------------(2)

Eqating (1) and (2)

$\frac{(170+x)}{21}$ $=\frac{2x}{15}$

$x=\frac{850}{9}$ $=94\frac{4}{9}$

From (2) $y=\frac{2x}{15}$ $=\frac{(2\times 850)}{(9\times 15)}$ $=12\frac{16}{27}$