If Rs.510 be divided among A, B and C in such a way that A gets $$\frac{2}{3}$$ of what B gets and B gets $$\frac{1}{4}$$ of what C gets, then their shares are respectively. 

Let A's share be 'A', B's share be 'B' and C's share be 'C'.

A=$$\frac{2}{3}\times B\Rightarrow$$ A:B=2:3$$\rightarrow$$ (1)

B=$$\frac{1}{4}\times C\Rightarrow$$ B:C=1:4$$\rightarrow$$ (2)

Multiplying equation(2) with 3
$$\Rightarrow$$ B:C=3:12 $$\rightarrow$$(3)

Combining equation(1) and equation(3)
$$\Rightarrow$$ A:B:C=2:3:12. Total parts = 2+3+12=17 parts

17 parts$$\rightarrow$$Rs.510
1 part$$\rightarrow$$Rs.30

A's share $$\rightarrow$$ 2 parts $$\rightarrow$$ Rs.60
B's share $$\rightarrow$$ 3 parts $$\rightarrow$$ Rs.90
C's share $$\rightarrow$$ 12 parts $$\rightarrow$$ Rs.360