P, Q and R jointly start a business. It was agreed that P would invest Rs. 25,000 for 6 months, Q Rs. 44,000 for 5 months and R Rs. 50,000 for 3 months. Out of total profit of Rs. 1,04,000, the amount received by P will be:

Correct option is A

Given:

P invests Rs. 25,000 for 6 months.
Q invests Rs. 44,000 for 5 months.
R invests Rs. 50,000 for 3 months.
The total profit is Rs. 1,04,000.

Formula Used:

$$\text{Share of Profit} = \frac{\text{Investment} \times \text{Time}}{\text{Total Capital}} \times \text{Total Profit}$$​
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​$$\text{Ratio of Profit Shares} = \left(P_{\text{investment}} \times P_{\text{time}}\right) : \left(Q_{\text{investment}} \times Q_{\text{time}}\right) : \left(R_{\text{investment}} \times R_{\text{time}}\right)$$

Solution:

Individual contributions:

​$$P = 25,000 \times 6 = 1,50,000 \\Q = 44,000 \times 5 = 2,20,000 \\R = 50,000 \times 3 = 1,50,000$$

$$P : Q : R = 1,50,000 : 2,20,000 : 1,50,000 = 15 : 22 : 15$$

Total profit = Rs. 1,04,000

​$$P_{\text{profit}} = \frac{15}{52} \times 1,04,000 \\\ \\P_{\text{profit}} = \frac{15 \times 1,04,000}{52} = 30,000$$ 

The amount received by P is Rs. 30,000.​​

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