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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 New Profit Sharing Ratio in this case is:

Solution

✅ Correct Option: 2

Old profit sharing ratio of A, B and C = 3:2:1

Converting to common denominator: A = 3/6, B = 2/6, C = 1/6

D is admitted for 1/4th share, which he acquires:

  • 1/8th from A
  • 1/8th from B

Calculating new shares:

A's new share = Old share - Sacrifice = 36−18\frac{3}{6} - \frac{1}{8}

Converting to common denominator (24):

A's new share = 1224−324=924\frac{12}{24} - \frac{3}{24} = \frac{9}{24}

B's new share = Old share - Sacrifice = 26−18\frac{2}{6} - \frac{1}{8}

Converting to common denominator (24):

B's new share = 824−324=524\frac{8}{24} - \frac{3}{24} = \frac{5}{24}

C's new share = Old share (no sacrifice) = 16=424\frac{1}{6} = \frac{4}{24}

D's new share = 18+18=14=624\frac{1}{8} + \frac{1}{8} = \frac{1}{4} = \frac{6}{24}

Verification: 924+524+424+624=2424=1\frac{9}{24} + \frac{5}{24} + \frac{4}{24} + \frac{6}{24} = \frac{24}{24} = 1 ✓

New Profit Sharing Ratio = 9:5:4:6

The answer is Option 2: 9:5:4:6

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