Two brother invested Rs. 50000 and Rs. 70000 respectively in a business and agreed that 70% of the profits should be divided equally between them and the remaining profit in the ratio of investment. If one brothers gets Rs. 90 more than the other. Find the total profit made in the business ?

Solution(By Examveda Team)

30% of the total profit is divided in the ratio 50000 : 70000 = 5 : 7 between the two partners.
Suppose x = 30% of the total profit. Then
$$\eqalign{ & x \times \frac{{7 - 5}}{{7 + 5}} = 90 \cr & x \times \frac{1}{6} = 90 \cr & x = 540 \cr & 30\% \,{\text{of}}\,{\text{the}}\,{\text{total}}\,{\text{profit}} = 540 \cr & {\text{Total Profit}} \cr & = \frac{{540 \times 100}}{{30}} \cr & = 1800 \cr} $$

Alternative
From the 30% of the profit, let first partner gets x and second partner gets (x + 90)
$$\eqalign{ & x:(x + 90) = 50000:70000 \cr & x:(x + 90) = 5:7 \cr & 7x = 5x + 450 \cr & 2x = 450 \cr & x = 225 \cr & \therefore 30\% \,{\text{of}}\,{\text{the}}\,{\text{profit}} \cr & = x + {\text{x}} + 90 \cr & = 225 + 225 + 90 \cr & = 540 \cr & {\text{Total Profit}} = \frac{{540 \times 100}}{{30}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1800 \cr} $$