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A, B and C are partners in a firm sharing profits in the ratio of 3:2:1. D is admitted into the firm for 1/4th share in profits, which he gets as 1/8th from A and 1/8th from B. The total capital of the firm is agreed upon as Rs. 1,20,000 and D is to bring in cash equivalent to 1/4th of this amount as his capital. The capitals of other partners are also to be adjusted in the ratio of their respective shares in profits. The capitals of A, B and C after all adjustments are Rs. 40,000, Rs. 35,000 and Rs. 30,000 respectively.

Required capitals of all partners is:

Solution

✅ Correct Option: 2

Finding the new profit sharing ratio:

Old ratio of A:B:C = 3:2:1

A's old share = 36\frac{3}{6}, B's old share = 26\frac{2}{6}, C's old share = 16\frac{1}{6}

D is admitted for 14\frac{1}{4} share, getting 18\frac{1}{8} from A and 18\frac{1}{8} from B.

New shares:

  • A = 36−18=1224−324=924\frac{3}{6} - \frac{1}{8} = \frac{12}{24} - \frac{3}{24} = \frac{9}{24}
  • B = 26−18=824−324=524\frac{2}{6} - \frac{1}{8} = \frac{8}{24} - \frac{3}{24} = \frac{5}{24}
  • C = 16=424\frac{1}{6} = \frac{4}{24} (unchanged)
  • D = 14=624\frac{1}{4} = \frac{6}{24}

New profit sharing ratio = A:B:C:D = 9:5:4:6


Calculating required capitals:

Total capital of firm = Rs. 1,20,000

Since capitals need to be adjusted in the new profit sharing ratio:

Required capital of A = 924×1,20,000\frac{9}{24} \times 1,20,000 = Rs. 45,000

Required capital of B = 524×1,20,000\frac{5}{24} \times 1,20,000 = Rs. 25,000

Required capital of C = 424×1,20,000\frac{4}{24} \times 1,20,000 = Rs. 20,000

Required capital of D = 624×1,20,000\frac{6}{24} \times 1,20,000 = Rs. 30,000

The information about actual capitals (Rs. 40,000, Rs. 35,000, Rs. 30,000) is given to determine subsequent adjustments, but the question asks for required capitals based on the new profit sharing ratio.

Answer: Option 2

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