A, B and C invested money in the ratio of $$\frac{1}{2}:\frac{1}{3}:\frac{1}{5}$$   in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?

Explanation:-

Ratio of capital invested by
$${\text{A, B and C}} = 15:10:6$$
Total capital invested by A in 1 year
$$\eqalign{ & = 15x \times 4 + 30x \times 8 \cr & = 300x \cr}$$
Total capital invested by B in 1 year
$$\eqalign{ & = 10x \times 6 + 5x \times 6 \cr & = 90x \cr}$$
Total capital invested by C in 1 year
$$\eqalign{ & = 6x \times 12 \cr & = 72x \cr}$$
Ratio of profits:

A	:	B	:	C
300x	:	90x	:	72x
50x	:	15x	:	12x

According to the question,
$$\Leftrightarrow \left( {50x + 15x + 12x} \right)$$     = $${\text{Rs}}{\text{. 34650}}$$
$$\eqalign{ & \Leftrightarrow 77x = {\text{Rs}}.{\text{ }}34650 \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}\frac{{34650}}{{77}} \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}450 \cr & {\text{Profit of A}} = {\text{Rs}}{\text{. }}450 \times 50 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 22500}} \cr & {\text{Profit of B}} = {\text{Rs}}{\text{. }}450 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6750}} \cr & {\text{Profit of C}} = {\text{Rs}}{\text{. }}450 \times 12 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 5400}} \cr}$$