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

Daksh's profit share is determined by the profit-sharing arrangement post-admission. The initial ratio among Arun, Bashir, and Joseph is 5:3:2. Arun contributes \( \frac{1}{5} \) of his portion to Daksh.

Calculation Breakdown:

1. Arun's Original Allocation:
   Arun's initial share = \( \frac{5}{10} \) (Total ratio sum = 5+3+2=10; Arun's part = 5)
2. Arun's Contribution:
   Arun's contribution is \( \frac{1}{5} \) of his share:
   \[ \text{Contribution} = \frac{1}{5} \times \frac{5}{10} = \frac{5}{50} = \frac{1}{10} \]
3. Daksh's Entitlement:
   Daksh receives this contributed portion, establishing his share as \( \frac{1}{10} \).

Therefore, Daksh's share of the firm's profits is \( \frac{1}{10} \).