Question

A and B are partners sharing profits in the ratio of \( 3:2 \). C is admitted as a new partner for a \( \frac{1}{5} \)th share in the profits, which he acquires entirely from A. What will be the new profit-sharing ratio of A, B, and C?

• A. \( 2:2:1 \)
• B. \( 3:2:1 \)
• C. \( 12:8:5 \)
• D. \( 4:3:1 \)

Hint:

Always read the exact wording of the sacrifice carefully. Phrases like "acquires entirely from" mean you perform a direct subtraction from that single partner, bypassing any multi-partner distribution steps.

Answer 1

The Correct Option is A

Concept: When a new partner is admitted, they acquire their profit share from the old partners. The sacrificing fraction is deducted exclusively from the specific old partners' existing shares to compute the new profit-sharing ratio.

Step 1: Calculate A's new profit share balance.
A's old share is \( \frac{3}{5} \). Since C acquires his entire share of \( \frac{1}{5} \) from A, we subtract this fraction directly from A: \[ \text{A's New Share} = \frac{3}{5} - \frac{1}{5} = \frac{2}{5} \]

Step 2: Determine B's new share and align denominators.
Since C acquired nothing from B, B's share remains completely unchanged: \[ \text{B's New Share} = \frac{2}{5} \] C's admitted share is explicitly given as: \[ \text{C's Share} = \frac{1}{5} \]

Step 3: Express the combined new profit-sharing ratio.
Combining the individual fractions \( \text{A} : \text{B} : \text{C} \): \[ \frac{2}{5} : \frac{2}{5} : \frac{1}{5} \quad \Rightarrow \quad 2:2:1 \]