A, B and C enter into a partnership. A contributes one-third of the capital while B contributes as much as A and C together contribute. If the profit at the end of the year amounts to Rs. 900, what would C receive ?

Explanation:-

$$\eqalign{ & {\text{Let total capital}} = {\text{Rs}}{\text{.}}\,{\text{x}} \cr & {\text{Then, A's capital}} = {\text{Rs}}{\text{.}}\,\frac{x}{3} \cr}$$
B's capital = (A + C)'s capital
(B's capital) = (A + B + C)'s capital = Rs. x
$$\eqalign{ & \Rightarrow {\text{B's capital}} = {\text{Rs}}{\text{.}}\frac{x}{2} \cr & \Rightarrow {\text{C's capital}} \cr & = {\text{Rs}}{\text{.}}\left[ {x - \left( {\frac{x}{3} + \frac{x}{2}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\,\frac{x}{6} \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}} \cr & = \frac{x}{3}:\frac{x}{2}:\frac{x}{6} \cr & = 2:3:1 \cr & {\text{So C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {900 \times \frac{1}{6}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{150}} \cr}$$