In a 200-metre race, 'P' beats 'Q' by 40 metres and 'Q' beats 'R' by 20 metres. By how much distance would 'P' beat 'R', in the same race?

We know that when time is constant, then ratio of speed is same as ratio of distance covered. So, distance covered by 'Q' when 'P' covered 200 metres = 200 - 40 = 160 metres So, ratio of speeds of 'P' and 'Q' = 200:160 = 5:4 And distance covered by 'R' when 'Q' covered 200 metres = 200 - 20 = 180 metres So, ratio of speeds of 'Q' and 'R' = 200:180 = 10:9 So, ratio of speeds of 'P', 'Q' and 'R' = 50:40:36 So, distance covered by 'R' in the time taken by 'P' to cover 200 metres = 200 × (36/50) = 144 metres So, 'P' beats 'R' by 200 - 144 = 56 metres Alternate Solution Ratio of speeds of 'P' and 'Q' = 200:(200 - 40) = 5:4 Ratio of speeds of 'Q' and 'R' = 200:(200 - 20) = 10:9 Ratio of speeds of 'P', 'Q' and 'R' = 50:40:36 So, required distance = {(50 - 36)/50} × 200 = 56 metres