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 calculate the new profit-sharing ratio: \[ {A's original share: } \frac{1}{2} \quad {B's share: } \frac{1}{3} \quad {C's share: } \frac{1}{4} \] The total ratio before admitting D: \[ {LCM of denominators: } 12 \implies \frac{6}{12} : \frac{4}{12} : \frac{3}{12} \] D is admitted for \( \frac{1}{6} \) share: \[ {D's share in terms of 12: } \frac{2}{12} \] This \( \frac{2}{12} \) share is deducted proportionately from A and B only: \[ {A's new share: } \frac{6}{12} - \frac{1}{12} = \frac{5}{12} \] \[ {B's new share: } \frac{4}{12} - \frac{1}{12} = \frac{3}{12} \] C retains his share of \( \frac{3}{12} \), and D has \( \frac{2}{12} \). The new ratio: \[ 5 : 3 : 3 : 2 \implies 21 : 14 : 15 : 10 \]