In a race of 300 metres, 'P' defeats 'R' by 45 metres, and

Solution

ATQ,

Let the time taken by 'P' to finish = t seconds

Then, distance covered by 'R' in t seconds = 300 - 45 = 255 metres

So, ratio of speeds of 'P' and 'R' = 300 : 255 = 20 : 17

Now, R beats Q by 30 metres, so:

Ratio of speeds of 'R' and 'Q' = 300 : (300 - 30) = 300 : 270 = 10 : 9

Now, combine:

Ratio of speeds of P, R, Q = 20×10 : 17×10 : 17×9 = 200 : 170 : 153

So, when 'P' runs 300 metres, 'Q' runs = 300 × (153/200) = 229.5 metres

Therefore, 'P' beats 'Q' by 300 - 229.5 = 70.5 metres