Question
In a 1000-metre race, 'Ravi' beats 'Shyam' by '200'
metres and 'Raj' by '300' metres. If 'Shyam' and 'Raj' participate in a 400-metre race, and 'Raj' gets a head start of 35 metres, then find the distance between 'Shyam' and 'Raj' when the winner reaches the finish line.Solution
ATQ, Ratio of speeds of 'Ravi', 'Shyam', and 'Raj' = 1000 : (1000 - 200) : (1000 - 300) = 10 : 8 : 7 So, ratio of speeds of Shyam and Raj = 8 : 7 Distance covered by 'Raj' in the time taken by 'Shyam' to cover 400 metres = 400 × (7/8) = 350 metres Total difference between 'Shyam' and 'Raj' when 'Shyam' reaches the finish line = 400 - (350 + 35) = 15 metres So, 'Shyam' will beat 'Raj' by 15 metres.
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