Question

In a 10 km race, A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C? ___

Answer 1

As given in the question, A is the winner and C is at the last among the three.
Also, A beat B by 1 km in 10 km run => Speed of A : Speed of B = 10 : 9
And, B beats C by 1 km in a 10 km run => Speed of B : Speed of C = 10 : 9
We have, A : B = 10 : 9
And B : C = 10 : 9
Multiplying 1st ratio by 10 and 2nd ratio by 9, we get A : B : C = 100 : 90 : 81
So, when A covers 10000 metres, C covers 8100 metres
Required answer = 10000 – 8100 = 1900 metres.