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 ₹ 900, what would C receive?

### Concept & Formula The profit in a partnership is distributed in proportion to the total capital invested and the time period of investment. When the time period is identical, profit is distributed based on the ratio of investments. $$Profit Ratio = Capital Ratio$$ ### Step-by-Step Solution 1. Let the total capital be $1$. 2. Capital contributed by A = $\frac{1}{3}$. 3. We are given that B contributes as much as A and C together: $B = A + C$. 4. Total capital is $A + B + C = 1$. 5. Substituting $B$ with $A + C$, we get: $A + (A + C) + C = 1$, which simplifies to $2(A + C) = 1$, so $A + C = \frac{1}{2}$. 6. Since A's share is $\frac{1}{3}$, C's share is: $C = \frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$. 7. Now, we find B's share: $B = A + C = \frac{1}{2}$. 8. The ratio of their investments (A : B : C) is $\frac{1}{3} : \frac{1}{2} : \frac{1}{6}$. Multiplying by 6 to clear denominators, we get 2 : 3 : 1. 9. C's share of the profit = $\frac{1}{6}$ of total profit = $\frac{1}{6} \times 900 = 150$. ### Exam Strategy & Shortcut Instead of finding B, recognize that if $B = A + C$, then B provides half the capital (since $A + B + C = 1$ implies $B + B = 1 \Rightarrow B = \frac{1}{2}$). Since A is $\frac{1}{3}$, C must make up the difference to half: $\frac{1}{2} - \frac{1}{3} = \frac{1}{6}$. The ratio is direct. ### Common Pitfall Misinterpreting "B contributes as much as A and C together" as B taking the majority of the profit without solving for C's specific fraction first. ### Final Answer Therefore, the correct answer is **₹ 150**.