Question
In a 1000 metres race, 'P' beats
'Q' by 150 metres, while 'Q' beats 'R' by 100 metres. Find the distance by which 'P' beats 'R' in the same race.Solution
Ratio of distance covered by 'P' to that of 'Q' = 1000:850 = 20:17 Ratio of distance covered by 'Q' to that of 'R' = 1000:900 = 10:9 Let the distance covered by 'Q' be '170x' metres. So, the distance covered by 'P' = (20/17) × 170x = '200x' metres Distance covered by 'R' = (9/10) × 170x = '153x' metres When 200x = 1000 So, x = 5 So, the distance covered by 'R' = 153 × 5 = 765 metres So, the distance by which 'P' beats 'R' = 1000 - 765 = 235 metres
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