Question

A and B are partners sharing profits in the ratio of 7 : 5. Their Capitals were ₹ 2,00,000 and ₹ 1,00,000, respectively. C is admitted into the partnership. C acquires his share of profit `1/24`th from A and `1/8`th from B. C does not pay anything for his share of goodwill. On C’s admission, the firm’s goodwill was valued at ₹ 90,000. Balance of A’s Capital Account will be ______.

Options

• ₹ 2,11,250

• ₹ 2,03,750

• ₹ 2,22,500

• ₹ 2,67,500

Answer 1

A and B are partners sharing profits in the ratio of 7 : 5. Their Capitals were ₹ 2,00,000 and ₹ 1,00,000, respectively. C is admitted into the partnership. C acquires his share of profit `1/24`th from A and `1/8`th from B. C does not pay anything for his share of goodwill. On C’s admission, the firm’s goodwill was valued at ₹ 90,000. Balance of A’s Capital Account will be ₹ 2,03,750.

Explanation:

Sacrifice Ratio of A and B = `1/24 : 1/8`

To simplify, use a common denominator of 24:

Sacrifice Ratio of A = `1/24`

Sacrifice Ratio of B = `1/8`

= `(1 xx 3)/(8 xx 3)`

= `3/24`

Sacrifice Ratio of A and B = `1/24 : 3/24` or 1 : 3

C’s share of Profit = `1/24 + 1/8`

= `1/24 + (1 xx 3)/(8 xx 3)`

= `1/24 + 3/24`

= `4/24`

= `1/6`

Firm’s Goodwill = ₹ 90,000

C’s share of Goodwill = `90,000 xx 1/6`

= ₹ 15,000

A’s share of Goodwill = `15,000 xx 1/4`

= ₹ 3,750

A’s Capital Account balance = 2,00,000 + 3,750

= ₹ 2,03,750