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    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 month
    Question

    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:

    A.

    Rs. 30,000

    B.

    Rs. 27,900

    C.

    Rs. 40,920

    D.

    Rs. 33,780

    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:

    Share of Profit=Investment×TimeTotal Capital×Total Profit\text{Share of Profit} = \frac{\text{Investment} \times \text{Time}}{\text{Total Capital}} \times \text{Total Profit}

    Ratio of Profit Shares=(Pinvestment×Ptime):(Qinvestment×Qtime):(Rinvestment×Rtime)\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=25,000×6=1,50,000Q=44,000×5=2,20,000R=50,000×3=1,50,000P = 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=15:22:15P : Q : R = 1,50,000 : 2,20,000 : 1,50,000 = 15 : 22 : 15

    Total profit = Rs. 1,04,000

    Pprofit=1552×1,04,000 Pprofit=15×1,04,00052=30,000P_{\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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