In a linear race of 500 m, A can beat B by 50 m and in a race of 600 m, B can beat C by 60 m. By how many metres will A beat C in a race of 400 m?

76

In this race, 

If A runs 500m, B runs 450m

Ratio of distance of A & B  = 10 : 9

If B runs 600m, C runs 540m

Ratio of distance of B & C  = 10 : 9

Similarly, if A runs 400m,

10R = 400 m

1R = 40

9R = 360 m

So , Distance run by B = 360 m

we know , Ratio of distance of B & C  = 10 : 9

10R = 360 m

1 R = 36

9R = 9 x 36 = 324 m

So ,  C will run  = 324 m

Thus, A will beat C by ( 400 - 324) = 76  m