In a 1000 metres race. A beats B by 40 seconds and B beats C by 20 seconds. If A beats C by 200 metres, then the time taken by A to cover 1 kilometre is :

4 minutes

The correct answer is Option (1) → 4 minutes

$t_A$ = time taken by A to complete the race

$t_B$ = time taken by B to complete the race

$t_C$ = time taken by C to complete the race

$t_B=t_A+40$

$t_C=t_B+20=t_A+60$

and,

$t_A=\frac{800}{1000}t_C=0.8t_C$

$∴t_A=0.8(t_B+20)$

$=0.8((t_A+40)+20)$

$=0.8(t_A+60)$

$⇒0.2t_A=48$

$⇒t_A=240\,seconds$