| A, B and C start a small business. A contributes one-fifth of the total capital invested in the business. B contributes as much as A and C together. Total profit at the end of the year was Rs. 5200. What was C's profit share? [SBI (PO) Pre 2015] |
A) Rs. 1510
B) Rs. 2510
C) Rs. 1500
D) Rs. 2560
E) Rs. 1560
Correct Answer: E
Solution :
| Let the total amount invested by A, B and C together be Rs. 100. |
| \[\therefore \] Amount invested by \[A=Rs.\frac{1}{5}\times 100\] |
| \[\Rightarrow \] \[A=Rs.\,20\] (i) |
| \[\therefore \] Amount invested by B and C together |
| \[=100-20\] |
| \[\Rightarrow \] \[(B+C)=Rs.\,80\] (ii) |
| Given, fi contributes as much as A and C together |
| \[\Rightarrow \] \[B=A+C\] ... (iii) |
| Using Eqs. (i), (ii) and (iii) |
| \[B=A+C\] |
| \[B-C=A\] |
| \[B-C=20\] (iv) |
| Given, \[B+C=80\] ... (v) |
| Solving Eqs. (iv) and (v), we get |
| \[\begin{matrix} B-C=20 \\ B+C=80 \\ 2B=100 \\ \end{matrix}\] |
| \[B=Rs.\,50\] |
| \[\therefore \] \[C=30\] |
| Now, ratio of investments of A, B and C |
| \[=20:50:30=2:5:3\] |
| Ratio of profits = Ratio of investments \[=2:5:3\] |
| Profit shared by \[C=\frac{3}{10}\times 5200=Rs.\,1560\] |
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