Question
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'?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
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