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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.

The capitals of other partners are also to be adjusted in the ratio of their respective shares in profits. A will bring in cash as capital after adjustment amount:

Solution

✅ Correct Option: 2

Looking at the given information:

Initial profit sharing ratio: A:B:C = 3:2:1

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

New profit sharing ratio:

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

New ratio = 9:5:4:6


Capital calculation:

Total capital = Rs. 1,20,000

D's capital = 14×1,20,000\frac{1}{4} \times 1,20,000 = Rs. 30,000

Remaining capital for A, B, and C = 1,20,000 - 30,000 = Rs. 90,000

This should be distributed in the ratio 9:5:4

  • A's required capital = 918×90,000\frac{9}{18} \times 90,000 = Rs. 45,000
  • B's required capital = 518×90,000\frac{5}{18} \times 90,000 = Rs. 25,000
  • C's required capital = 418×90,000\frac{4}{18} \times 90,000 = Rs. 20,000

Adjustment required:

Given that after adjustments, A's capital is Rs. 40,000

A's required capital = Rs. 45,000

A's actual capital = Rs. 40,000

Amount A needs to bring in = 45,000 - 40,000 = Rs. 5,000

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