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 :
Answer & explanation
Correct answer: option 1
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,
$t_A=\frac{800}{1000}t_C=0.8t_C$
$∴t_A=0.8(t_B+20)$
$=0.8((t_A+40)+20)$
$=0.8(t_A+60)$
$⇒0.2t_A=48$
$⇒t_A=240\,seconds$