In a race of one kilometre. A gives B a start of 100 metres and still wins by 20 seconds. But if A gives B a start of 25 seconds, B wins by 50 metres. The time taken by A to run kilometre is :

Solution(By Examveda Team)

Let the time taken by A to run 1000 metres = x seconds
Time taken by B to sun 900 metres = x + 20 seconds
Speed of A and B :
$$ = \frac{{1000}}{x},\frac{{900}}{{x + 20}}$$   respectively
According to the question,
$$\frac{{950}}{{\frac{{1000}}{x}}} - \frac{{1000}}{{\frac{{900}}{{x + 20}}}} = 25$$
(As B is the winner now)
$$\eqalign{ & \Rightarrow \frac{{950x}}{{1000}} - \frac{{1000\left( {x + 20} \right)}}{{900}} = 25 \cr & \Rightarrow \frac{{19x}}{{20}} - \frac{{10x + 200}}{9} = 25 \cr & \Rightarrow 171x - 200x - 4000 = 25 \times 20 \times 9 \cr & \Rightarrow 29x = 500 \cr & \Rightarrow x = \frac{{500}}{{29}}{\text{sec}} \cr} $$