Question
In a 500-metre race, 'M' beats 'O' by 100 metres, and 'O'
beats 'N' by 75 metres. Find by how much distance 'M' beats 'N'.Solution
ATQ,
Let time taken by 'M' to complete the race = t seconds
Then, 'O' covers = 500 - 100 = 400 metres
So, ratio of speeds of 'M' and 'O' = 500 : 400 = 5 : 4
'O' beats 'N' by 75 metres:
So, speed ratio of 'O' and 'N' = 500 : (500 - 75) = 500 : 425 = 20 : 17
Combining:
M : O : N = 5×20 : 4×20 : 4×17 = 100 : 80 : 68
When 'M' runs 500 metres, 'N' runs = 500 × (68/100) = 340 metres
Hence, 'M' beats 'N' by 500 - 340 = 160 metres
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