In a race of 300 metres, 'P' defeats 'R' by 45 metres, and 'R' defeats 'Q' by 30 metres. Find out how many metres 'P' defeats 'Q' by.

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