Question

A, B and C were partners in a firm sharing profits and losses in the ratio of \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \). D was admitted in the firm for \( \frac{1}{6} \) share. C would retain his original share. The new profit sharing ratio will be:

• A. 12 : 8 : 5 : 5
• B. 21 : 14 : 18 : 12
• C. 21 : 14 : 15 : 10
• D. 2 : 2 : 1 : 1

Hint:

When calculating new profit-sharing ratios, ensure to properly account for the portions deducted from existing partners as per the question's conditions.

Answer 1

The Correct Option is C

To determine the new profit-sharing ratio, the initial shares are: A's original share: \( \frac{1}{2} \), B's share: \( \frac{1}{3} \), C's share: \( \frac{1}{4} \). The total ratio before D's admission is found by calculating the LCM of the denominators: \( 12 \), resulting in the ratio \( \frac{6}{12} : \frac{4}{12} : \frac{3}{12} \). D is admitted for a \( \frac{1}{6} \) share, which is equivalent to \( \frac{2}{12} \). This \( \frac{2}{12} \) share is deducted proportionally from A and B. A's new share becomes \( \frac{6}{12} - \frac{1}{12} = \frac{5}{12} \). B's new share becomes \( \frac{4}{12} - \frac{1}{12} = \frac{3}{12} \). C retains their share of \( \frac{3}{12} \), and D has \( \frac{2}{12} \). The new ratio is \( 5 : 3 : 3 : 2 \), which simplifies to \( 21 : 14 : 15 : 10 \).