In a race of 300m, B gives a start of 30m to A and C gives a start of 60m to B. The start, that C can give to A in the same race.

84m

1st condition:

Ratio of distance covered ⇒ A : B = 270 : 300 = 9 : 10

2nd condition:

Ratio of distance covered ⇒ B : C = 240 : 300 = 4 : 5

Now,

   A    :   B    :   C

  9    :   10

             4    :   5

36   :  ----  :   50

50R = 300

1R = 6 

36R = 216m

Here we can see that, if C covers 300 m then A covers 216 m.

Therefore,

C gives ⇒ 300 - 216 = 84m start to A in the same race.