In a 1000 metres race, 'P' beats

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