Victor and Raymond are partners in a business sharing profits and losses in the ratio of 3… — JAMB UTME

Victor and Raymond are partners in a business sharing profits and losses in the ratio of $3:2$ . They admit Kenneth as a new partner, and the new profit-sharing ratio among Victor, Raymond, and Kenneth is agreed at $5:3:2$ . Kenneth pays $\text{₦}24,000$ in cash as premium for goodwill. What amount of the goodwill premium (in Naira) should be credited to Victor's capital account?

Answer: 12000 ₦

Answer

The amount of goodwill premium credited to Victor's capital account is ₦12,000.

Goodwill premium paid by a newly admitted partner is credited to existing partners in their sacrificing ratio. Victor's sacrifice is 3/5 - 5/10 = 1/10, and Raymond's sacrifice is 2/5 - 3/10 = 1/10. Since both partners sacrificed equally (1:1 ratio), Victor receives half of the ₦24,000 premium, which equals ₦12,000.

Step-by-Step Solution

Calculate the old shares of existing partners with a common denominator

Victor's old share = 3/5 = 6/10; Raymond's old share = 2/5 = 4/10

Aligning denominators makes sacrifice calculation straightforward.

Calculate individual partner sacrifice

Victor's sacrifice = 6/10 - 5/10 = 1/10; Raymond's sacrifice = 4/10 - 3/10 = 1/10

Sacrifice is the difference between old profit share and new profit share.

Determine sacrificing ratio

Sacrificing ratio = 1 : 1

Goodwill brought in by an incoming partner compensates existing partners in proportion to their sacrifice.

Compute Victor's share of goodwill premium

Victor's share = 1/2 × ₦24,000 = ₦12,000

Victor is entitled to half of the premium paid based on the 1:1 sacrificing ratio.

Key Concept

Allocation of Goodwill Premium upon Admission of a Partner

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