In a 400 metres race, 'X' defeats 'Z' by 80 metres and 'Z' defeats 'Y' by 50 metres. By how many metres does 'X' beat 'Y'?

ATQ,

Let the time taken by 'X' to complete the race = 't' seconds

Distance run by 'X' in t seconds = 400 metres

Distance run by 'Z' in 't' seconds = 400 - 80 = 320 metres

So, the ratio of speeds of 'X' and 'Z' = 400 : 320 = 5 : 4

Similarly, since 'Z' beats 'Y' by 50 metres:

Ratio of speeds of 'Z' and 'Y' = 400 : (400 - 50) = 400 : 350 = 8 : 7

Now, combine ratios to get:

Ratio of speeds of 'X', 'Z', 'Y' = 5×8 : 4×8 : 4×7 = 40 : 32 : 28

So, when 'X' finishes 400 metres, 'Y' covers = 400 × (28/40) = 280 metres

Therefore, 'X' beats 'Y' by 400 - 280 = 120 metres