P, Q and R are partners in a business. P receives $\frac{3}{5}$ of total profit while Q and R share the remaining profit equally. P's profit is increased by ₹1,800 when the rate of profit is increased from 10% to 13% in a year. Then R's share in total profit is:
Answer & explanation
Correct answer: option 4
$\text{P gets } \frac{3}{5} \text{ of total profit}$
$\text{Increase in rate} = 13\% - 10\% = 3\%$
$\text{Increase in total profit} = 3\% \text{ of capital}$
$\text{P's increase} = \frac{3}{5} \times 3\% \text{ of capital} = 1800$
$\frac{9}{5}\% \text{ of capital} = 1800$
$\frac{9}{5} \cdot \frac{1}{100} \cdot C = 1800$
$\frac{9C}{500} = 1800 \Rightarrow C = 100000$
$\text{Total profit at 13\%} = 13000$
$\text{Remaining for Q and R} = \frac{2}{5} \times 13000 = 5200$
$\text{R's share} = \frac{5200}{2} = 2600$
$\text{R's share} = ₹2600$