A, B and C become partners in a business. A contributes 1/3 rd of the capital for 1/4 th of the time. B contributes 1/5 th of the capital for 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 ?

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 = $$\frac{1}{3}\times 15$$   = 5units
Capital Investment of B = $$\frac{1}{5}\times 15$$   = 3units
Capital Investment of C = 15 - (5 + 3) = 7

A's Capital Invested for time = $$\frac{1}{4}\times 12$$   = 3units
B's Capital Invested for time = $$\frac{1}{6}\times 12$$   = 2units
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)
$$\begin{array}{rl}& \text{35 units}=\text{Rs}\text{. 1820}\\ & \text{1 unit}=\frac{1820}{35}=\text{Rs}.52\\ & \text{Hence A’s share in profit}\\ & =5\text{ units}\\ & =52\times 5\\ & =\text{Rs}\text{. 260}\end{array}$$