A, B and C started a business by investing $$\frac{1}{2}$$, $$\frac{1}{3^{rd}}$$ and $$\frac{1}{6^{th}}$$ of the capital respectively. After $$\frac{1}{3^{rd}}$$ of the total time, A withdrew his capital completely and after $$\frac{1}{4^{th}}$$ of the total time B withdrew his capital. C kept his capital for the full period. The ratio in which total profit is to be divided amongst the partners is

Assuming the total capital = 6 units and the total period = 12 months

Investment of A = 6*$$\ \frac{\ 1}{2}$$ = 3 units

Investment period of A = 12*$$\ \frac{\ 1}{3}$$ = 4 month

Investment of A = 6*$$\ \frac{\ 1}{3}$$ = 2 units

Investment period of A = 12*$$\ \frac{\ 1}{4}$$ = 3 months

Investment of A = 6*$$\ \frac{\ 1}{6}$$ = 1unit

Investment period of A = 12 months

Then the profit will be divided in the ratio (3*4):(2*3):(1*12) = 12:6:12 = 2:1:2