Question
In a 250 metres race, 'K' beats 'M' by 50 metres, and 'M'
beats 'L' by 20 metres. By how many metres does 'K' beat 'L'?Solution
ATQ,
Time taken by 'K' to finish = t seconds
Then, 'M' covers = 250 - 50 = 200 metres
So, ratio of speeds of 'K' and 'M' = 250 : 200 = 5 : 4
Now, 'M' beats 'L' by 20 metres:
Speed ratio of 'M' and 'L' = 250 : (250 - 20) = 250 : 230 = 25 : 23
Combining:
K : M : L = 5×25 : 4×25 : 4×23 = 125 : 100 : 92
When 'K' runs 250 metres, 'L' covers = 250 × (92/125) = 184 metres
So, 'K' beats 'L' by 250 - 184 = 66 metres
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