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 ?

Explanation:-

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