New Ratios

Correct answer: A. 4/10

The total ratio is 10, so D’s share is 4/10 and C’s old share is 3/10. D’s share is acquired by A, B and C in the ratio 1:2:1; therefore, C receives 1 out of 4 parts, i.e. (1/4) × (4/10) = 1/10. Hence, C’s new share is 3/10 + 1/10 = 4/10. Option B is incorrect because 3/10 is only C’s old share. Exam tip: Multiply the deceased or retiring partner’s share by the acquiring partner’s fraction of the gaining ratio.

Correct answer: A. Total future profit is shared in 5:3, and the additional share is acquired in 1:2

The governing concept is the distinction between the new profit-sharing ratio and the gaining ratio after retirement. The new ratio describes the complete shares of the continuing partners in all future profits; therefore, future profit is divided in the ratio 5:3. The gaining ratio describes only the additional portions obtained by the continuing partners from the retiring partner. Thus, 1:2 cannot be used to distribute the entire future profit. It is used only to determine how the retired partner’s former share is acquired. Option A correctly states both functions, while B confuses the two ratios, C makes a false generalisation, and D incorrectly gives future profit to the retiring partner.

Correct answer: A. Old share plus the given gained share

The governing concept is the meaning of a gain after retirement or death of a partner. A continuing partner receives an additional portion of the retiring or deceased partner’s share. Consequently, the partner’s final or new share must include both components: the share originally held and the extra share acquired. In symbols, new share = old share + gained share. For example, if a partner originally has 3/10 and gains 1/10, the new share is 4/10, not 2/10 or 1/10. Option A expresses this rule accurately. Option B would reduce the partner’s entitlement, C ignores the original ownership, and D ignores the benefit received from the outgoing partner.