 ### A, B and C become partners in a business. A contributes $\Large\frac{1}{3}$rd of the capital for $\Large\frac{1}{4}$th of the time. B contributes $\Large\frac{1}{5}$th of the capital for $\Large\frac{1}{6}$th of the time and C the rest of the capital for the whole time. If the profit is Rs. 1820, then the A’s share in profit is ?

A. Rs. 130 B. Rs. 260 C. Rs. 292 D. Rs. 304 Answer: Option B
Let the total capital of A, B and C = 15 units Let total time for investment = 12 units Now, According to the question, Capital Investment of A = $\Large\frac{1}{3}$$\times 15=5 units Capital Investment of B = \Large\frac{1}{5}$$\times 15=3$ units Capital Investment of C = 15 – (5 + 3) = 7 A’s Capital Invested for time = $\Large\frac{1}{4}$$\times 12=3 units B’s Capital Invested for time = \Large\frac{1}{6}$$\times 12=2$ units C’s Capital Invested all the time. i.e = 12units ∴ Profit ratio of A : B : C = (5 × 3) : (3 × 2) : (7 × 12) = 15 : 6 : 84 = 5 : 2 : 28 Total profit = 5 + 2 + 28 = 35 units Also, total profit = Rs. 1820 (given) \begin{aligned}&35\text{ units }=\text{ Rs. }1820\\ &1\text{ unit }=\frac{1820}{35}=Rs.52\end{aligned} Hence, A’s share in profit $\begin{array}{l} =5 \text { units } \\ =52 \times 5 \\ =\text { Rs. } 260 \end{array}$