Question

Arun, Bashir and Joseph were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. They admitted Daksh as a new partner who acquired his share entirely from Arun. If Arun sacrificed \( \frac{1}{5} \)th from his share to Daksh, Daksh's share in the profits of the firm will be :

• A. \( \frac{1}{5} \)
• B. \( \frac{1}{10} \)
• C. \( \frac{3}{10} \)
• D. \( \frac{2}{5} \)

Hint:

The share sacrificed by the old partner(s) directly becomes the share of the new partner. When a specific fraction is mentioned as being sacrificed "to" the new partner, that fraction usually represents the new partner's share of the total profit.

Answer 1

The Correct Option is B

To determine Daksh's share in the profits, we need to understand the profit-sharing arrangement after Daksh is admitted. The original profit-sharing ratio among Arun, Bashir, and Joseph is 5:3:2. Arun sacrifices \( \frac{1}{5} \)th of his share to Daksh.

Step-by-step Calculation:

1. Original Share of Arun:
   Arun's original share = \( \frac{5}{10} \) (since total ratio sum = 5+3+2=10, Arun's part is 5)
2. Arun's Sacrifice:
   Arun sacrifices \( \frac{1}{5} \) of his share:
   \[ \text{Sacrifice} = \frac{1}{5} \times \frac{5}{10} = \frac{5}{50} = \frac{1}{10} \]
3. Daksh's Share:
   Daksh acquires this sacrificed share, so his share is \( \frac{1}{10} \).

Hence, Daksh's share in the profits of the firm will be \( \frac{1}{10} \).