NCHMCT JEE 2014 Question Paper with solutions for online practice

Let speeds of A, B and C are x, y and z respectively.
Then from question,
$\frac{600}{\mathit{x}}$ = $\frac{600-60}{\mathit{y}}$
⇒ $\frac{\mathit{x}}{\mathit{y}}$ = $\frac{10}{9}$ ... (i)
and $\frac{500}{\mathit{y}}$ = $\frac{500-50}{\mathit{z}}$
⇒ $\frac{\mathit{y}}{\mathit{z}}$ = $\frac{10}{9}$ ... (ii)
from (i) and (ii), we have
$\frac{\mathit{x}}{\mathit{z}}$ = $\frac{10}{81}$ ... (iii)
Again, suppose that A beat C in a race of 400 metres by a distance w metres.
Then,
$\frac{400}{\mathit{x}}$ = $\frac{400\mathit{w}}{\mathit{z}}$
400 - w = $\frac{400\times \mathit{z}}{\mathit{x}}$
= $\frac{400\times 81}{100}$
= 324
∴ w = 400 - 324
= 76 metres