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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.

C will withdraw the capital amount after capital are adjusted in the ratio of their respective shares in profits. The amount is:

Solution

✅ Correct Option: 3

Finding D's share and new profit sharing ratio:

D gets 1/4th share by taking:

  • 1/8 from A
  • 1/8 from B

Old ratio of A:B:C = 3:2:1 (total 6 parts)

A's old share = 3/6 = 1/2, B's old share = 2/6 = 1/3, C's old share = 1/6

After D's admission:

  • A's new share = 1/2 - 1/8 = 3/8
  • B's new share = 1/3 - 1/8 = 5/24
  • C's new share = 1/6 (unchanged)
  • D's new share = 1/4

Converting to ratio with common denominator 24:

  • A = 9/24
  • B = 5/24
  • C = 4/24
  • D = 6/24

New profit sharing ratio = 9:5:4:6


Capital adjustment:

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

C's required capital based on new ratio = 424×1,20,000\frac{4}{24} \times 1,20,000 = Rs. 20,000

C's actual capital after adjustments (given) = Rs. 30,000

Amount C will withdraw = Rs. 30,000 - Rs. 20,000 = Rs. 10,000

Since C's actual capital (Rs. 30,000) exceeds the required capital (Rs. 20,000) based on the new profit sharing ratio, C needs to withdraw the excess amount.

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