A and B started a business jointly. A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received Rs. 4000 as profit, then their total profit is ?
Correct Answer: Rs. 28000
Suppose B invested Rs. x for y months
Then, A invested Rs. 3x for 2y months
$$\eqalign{ & {\text{So, A}}:{\text{B}} \cr & = \left( {3x \times 2y} \right):\left( {x \times y} \right) \cr & = 6xy:xy \cr & = 6:1 \cr & \therefore {\text{B's profit}}:{\text{Total profit}} = 1:7 \cr & {\text{Let the total profit is Rs}}{\text{. }}x \cr & {\text{Then,}}\frac{1}{7} = \frac{{4000}}{x} \cr & \Leftrightarrow x = 28000 \cr} $$
Then, A invested Rs. 3x for 2y months
$$\eqalign{ & {\text{So, A}}:{\text{B}} \cr & = \left( {3x \times 2y} \right):\left( {x \times y} \right) \cr & = 6xy:xy \cr & = 6:1 \cr & \therefore {\text{B's profit}}:{\text{Total profit}} = 1:7 \cr & {\text{Let the total profit is Rs}}{\text{. }}x \cr & {\text{Then,}}\frac{1}{7} = \frac{{4000}}{x} \cr & \Leftrightarrow x = 28000 \cr} $$