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L and M are partners sharing profits in the ratio 3:2. N is admitted as a partner for 1/5th of the share which is acquired from L. Goodwill of the firm is valued at Rs. 40,000 on N's admission. N will have to pay for Goodwill:

Solution

✅ Correct Option: 2

Initial Profit Sharing Ratio:

L and M share profits in the ratio 3:2

This means:

  • L's share = 35\frac{3}{5}
  • M's share = 25\frac{2}{5}

N's Admission:

N is admitted for 15\frac{1}{5}th share, which is acquired entirely from L (not from both partners).


New Profit Sharing Ratio:

  • L's new share = 35−15=25\frac{3}{5} - \frac{1}{5} = \frac{2}{5}
  • M's share = 25\frac{2}{5} (remains unchanged as M doesn't sacrifice)
  • N's share = 15\frac{1}{5}

Sacrificing Ratio:

Since N acquires the entire share only from L:

  • L's sacrifice = 15\frac{1}{5}
  • M's sacrifice = 0 (M doesn't sacrifice any share)

Goodwill Payment:

Goodwill of the firm = Rs. 40,000

N's share in goodwill = N's share × Total Goodwill

N's share in goodwill = 15×40,000\frac{1}{5} \times 40,000 = Rs. 8,000

Since N acquired the entire 15\frac{1}{5}th share from L alone, N will pay Rs. 8,000 to L only.

Correct Option: 2 (Rs. 8,000 to L)

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