A, B and C are partners in a business. Their shares are in the proportion of $$\frac{1}{3}:\frac{1}{4}:\frac{1}{5}$$ . A withdraws half of his capital after 15 months and after another 15 months, a profit of Rs. 4340 is divided. The share of C is ?

Explanation:-

Ratio of initial investments
$$\eqalign{ & = \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \cr & = 20:15:12 \cr}$$
Let their initial investments be 20x, 15x and 12x respectively
$$\eqalign{ & = {\text{A}}:{\text{B}}:{\text{C}} \cr & = \left( {20x \times 15 + 10x \times 15} \right):\left( {15x \times 30} \right):\left( {12x \times 30} \right) \cr & = 450x:450x:360x \cr & = 5:5:4 \cr & \therefore {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {4340 \times \frac{4}{{14}}} \right) \cr & = {\text{Rs. }}{\text{1240}} \cr}$$