X and Y share profits and losses in the ratio of 2 : 1. They take Z as a…
2024
X and Y share profits and losses in the ratio of 2 : 1. They take Z as a partner and the new profit sharing ratio becomes 3 : 2 : 1. Z brings Rs. 4,500 as premium for goodwill. What will be the value of the firm’s goodwill?
- A.
Rs. 4,500
- B.
Rs. 18,000
- C.
Rs. 27,000
- D.
Rs. 24,000
Attempted by 7 students.
Show answer & explanation
Correct answer: C
Concept: When a new partner is admitted, the premium (goodwill) they pay corresponds to their own share of profit in the new ratio. This gives the relationship: Total Goodwill = Premium paid by the new partner ÷ New partner's share of profit.
X and Y originally shared profits in the ratio 2 : 1. After admitting Z, the new profit-sharing ratio becomes 3 : 2 : 1 (X : Y : Z).
Total parts in the new ratio = 3 + 2 + 1 = 6, so Z's share of profit = 1/6.
Z brings Rs. 4,500 as premium for goodwill, and this amount represents his 1/6 share of the firm's total goodwill.
Applying the relationship: Total goodwill = Premium ÷ Z's share = 4,500 ÷ (1/6) = 4,500 × 6 = Rs. 27,000.
Cross-check: If the total goodwill is Rs. 27,000, Z's 1/6 share equals 27,000 ÷ 6 = Rs. 4,500, which matches the given premium — confirming the value.