Two partners invested Rs. 125000 and Rs. 85000 respectively in a business. They distribute 60% of the profit equally and decide to distribute the remaining 40% as the interest on their capitals. If one partner received Rs. 3000 more than the other, the total profits is ?

Answer: Option B

$$\begin{array}{rl}& \text{Let the total profit be Rs}\text{. }x\\ & \text{Then, }60\%\text{ of the profit}\\ & =\text{Rs}\text{.}\left(\frac{60}{100}\times x\right)\\ & =\text{Rs}\text{.}\frac{3x}{5}\end{array}$$
From this part of the profit each gets = $$\text{Rs}\text{.}\frac{3x}{10}$$
$$\begin{array}{rl}& 40\%\text{ of total profit }\\ & =\text{Rs}\text{.}\left(\frac{40}{100}\times x\right)\\ & =\text{Rs}\text{.}\frac{2x}{5}\end{array}$$
Now, this amount of Rs. $$\frac{2x}{5}$$ has been divided in the ratio of capitals, which is 125000 : 85000 or 25 : 17 as interests
∴ Interest on first capital
$$\begin{array}{rl}& =\text{ Rs}\text{.}\left(\frac{2x}{5}\times \frac{25}{42}\right)\\ & \text{ = Rs}\text{.}\frac{5x}{21}\end{array}$$
Interest on second capital
$$\begin{array}{rl}& =\text{Rs}\text{.}\left(\frac{2x}{5}\times \frac{17}{42}\right)\\ & \text{ = Rs}\text{.}\frac{17x}{105}\end{array}$$
Total money received by first partner
$$\begin{array}{rl}& =\text{Rs}\text{.}\left(\frac{3x}{10}+\frac{5x}{21}\right)\\ & \text{ = Rs}\text{.}\frac{113x}{210}\end{array}$$
Total money received by second partner
$$\begin{array}{rl}& =\text{Rs}\text{.}\left(\frac{3x}{10}+\frac{17x}{105}\right)\\ & \text{ = Rs}\text{.}\frac{97x}{210}\\ & \therefore \frac{113x}{210}-\frac{97x}{210}=3000\\ & \Rightarrow x=39375\\ & \text{Hence,}\\ & \text{Total profit Rs}\text{. 39375}\end{array}$$