In a 400 metres race, 'X' defeats 'Z' by 80 metres and

Solution

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