Multiple choice

Three partners X, Y and Z start a business. Initially, X contributes Rs. 2500, Y contributes Rs. 3000 and Z contributes Rs. 1500. After 7 months, Y withdraws Rs. 1000, while at the end of 8 months, Z further invests Rs. 2000. The total profit at the end of the year is Rs. 5568. How should this profit be divided (in Rs.) among the partners, respectively?

  1. Rs. 1920, Rs. 1984 and Rs. 1664

  2. Rs. 1900, Rs. 1300 and Rs. 2368

  3. Rs. 1919, Rs. 2172 and Rs. 1477

  4. None of these
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A Correct answer
Explanation

Calculate the equivalent investment for one month for each partner. X: 2500*12 = 30000. Y: (3000*7) + (2000*5) = 21000 + 10000 = 31000. Z: (1500*8) + (3500*4) = 12000 + 14000 = 26000. Ratio X:Y:Z = 30:31:26. Total parts = 87. Profit per part = 5568/87 = 64. X gets 30*64 = 1920, Y gets 31*64 = 1984, Z gets 26*64 = 1664.

AI explanation

The ratio of profit is calculated using the formula for effective capital, which is investment multiplied by time. The effective capital for X is 2500 multiplied by 12 to equal 30000, for Y it is (3000 times 7) plus (2000 times 5) to equal 31000, and for Z it is (1500 times 8) plus (3500 times 4) to equal 26000. The profit sharing ratio of X to Y to Z is 30000 to 31000 to 26000, which simplifies to 30 to 31 to 26. The total of these ratio parts is 87, and since the total profit is 5568, the value of one part is 5568 divided by 87, which equals 64. The individual profit shares are found by multiplying this base value by their respective ratio parts: X gets 30 times 64 to equal 1920, Y gets 31 times 64 to equal 1984, and Z gets 26 times 64 to equal 1664.

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