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    A and B started a business by investing Rs.2,400 and Rs. 3,600 respectively. At the end of 4th month from the start, C joined with Rs. x. After 8 mont
    Question

    A and B started a business by investing Rs.2,400 and Rs. 3,600 respectively. At the end of 4th month from the start, C joined with Rs. x. After 8 months from start of the business, B withdrew Rs. 600. If C's share is Rs. 8,000 in annual profit of Rs. 22,500 then amount invested by Cis:

    A.

    Rs. 4,800

    B.

    Rs. 7,200

    C.

    Rs. 5,800

    D.

    Rs. 4,000

    Correct option is A

    Given:

    Investment by A = Rs 2400

    Investment by B = Rs 3600

    After the 4th month, C joined with Rs x.

    After 8 months, B withdrew Rs 600 from the business.

    Total annual profit = Rs 22,500

    C's share = Rs 8000

    Formula Used:

    Profit Share = Amount Invested × Duration of Investment

    Solution:

    Total duration for which A invested: 1 year = 12 months

    B invested Rs 3600 for 8 months, and then Rs (3600 - 600) = 3000 for 4 months

    C invested Rs x for 8 months.

    Profit share of A, B, and C in ratio:

    (2400×12) : (3600×8 + 3000×4) : (x×8)

    Simplify:

    A's share: 2400×12 = 28800

    B's share: 3600 × 8 + 3000 × 4 = 28800 + 12000 = 40800

    C's share: x × 8 = 8x

    Total profit = Rs 22,500. C's share:

    8x28800+40800+8x×22500=8000\frac{8x}{28800 + 40800 + 8x} \times 22500 = 8000

    Simplify: 8x69600+8x=800022500Cross multiply: 45×8x=16×(69600+8x)45x=16×69600+16x45x16x=111360029x=1113600x=111360029=4800C’s investment: Rs 4800\text{Simplify: } \\\frac{8x}{69600 + 8x} = \frac{8000}{22500} \\\text{Cross multiply: } \\45 \times 8x = 16 \times (69600 + 8x) \\45x = 16 \times 69600 + 16x \\45x - 16x = 1113600 \\29x = 1113600 \\x = \frac{1113600}{29} = 4800 \\\text{C's investment: Rs } 4800​​

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