In a 4 km race, A, B, and C, each running at uniform speed, secured first, second, and third position, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many meters does A beat C in the same race?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1750 m
A beats B by 1 km, which means when A completes the race by traveling 4 km B would have covered 3 km.
⇒The ratio of speeds of A and B = 4 : 3.
B beats C by 1 km, which means when B completes the race by traveling 4 km, C would have covered 3 km.
⇒The ratio of speeds of B and C = 4 : 3
⇒A : B = 4 : 3
⇒B : C = 4 : 3
⇒The ratio of speeds of A : B : C = 16 : 12 : 9
When A travels 16 m, C travels 9 m.
⇒Time taken by A to cover 4km = 4000/16 = 250 s
⇒Distance covered by C in 250 s = 9(250) = 2250 m
⇒A would beat C by = 4000 - 2250 = 1750 m.