A, B and C started a business by investing Rs. 27,500, Rs. 32,500 and Rs 37,500 respectively A is a working partner and gets 20% of the profit as working allowance and remaining is distributed in the proportion of their investment. If the money received by C is Rs. 13,500, what is the total profit?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let total profit}} = 100{\text{ unit}} \cr & 20\% {\text{ taken by C remaining profit}} \cr & = \frac{{100 \times 80\% }}{{100}} \cr & = 80{\text{ unit}} \cr & {\text{Ratio of money}} \cr} $$
\[\begin{array}{*{20}{c}} {\text{A}}&:&{\text{B}}&:&{\text{C}}&{} \\ {27,500}&{}&{32,500}&{}&{37,500}&{} \\ {11}&:&{13}&:&{15}&{ = 39{\text{ unit}}} \\ {}&{}&{}&{}&\begin{gathered} \,\,\,\,\,\,\,\,\,\, \downarrow _{39}^{ \times 80} \hfill \\ \hfill \\ \end{gathered} &\begin{gathered} \,\,\,\,\, \downarrow \hfill \\ \,\,\,\,80{\text{ unit}} \hfill \\ \end{gathered} \end{array}\]
$$\eqalign{ & \frac{{400}}{{13}}{\text{ unit}} = 13500 \cr & 1{\text{ unit}} = \frac{{135 \times 13}}{4} \cr & 100{\text{ unit}} = 135 \times 13 \times 25 = 43,875 \cr & {\text{Total profit}} = {\text{ Rs}}{\text{. 43,875}} \cr} $$