A, B and C started a business by investing Rs. 24000, Rs. 32000 and Rs. 18000 respectively. A and B are active partners and get 15% and 12% of total profit and remaining profit is to be distributed among them in the ratio of their investment. If C got total Rs. 65700 as a profit, what was the total amount of profit ?

Explanation:-

	A	:	B	:	C
Capital →	24000	:	32000	:	18000
	24	:	32	:	18
	12	:	16	:	9

$$\eqalign{ & {\text{Let the total profit}} = 100x \cr & {\text{Extra share of A}} \cr & = 100x \times \frac{{10}}{{100}} \cr & = 15x \cr & {\text{Extra share of B}} \cr & = 100x \times \frac{{12}}{{100}} \cr & = 12x \cr & {\text{Remaining profit}} \cr & = \left[ {100x - \left( {15x + 12x} \right)} \right] \cr & = 73x \cr}$$
According to the question,
Note: Remaining profit will be distributed in the ratio of their capitals.
∴ Share of C
$$\eqalign{ & \Leftrightarrow \frac{{73x}}{{\left( {12 + 16 + 9} \right)}} \times 9 = {\text{Rs}}{\text{. }}65700 \cr & \Leftrightarrow \frac{{657x}}{{37}} = {\text{Rs}}{\text{. }}65700 \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}\frac{{65700 \times 37}}{{657}} \cr & \Leftrightarrow x = {\text{Rs}}{\text{. 3}}700 \cr & {\text{Hence, required profit}} \cr & = 100x \cr & = 100 \times 3700 \cr & = {\text{Rs}}{\text{. 3}}70000 \cr}$$