Question

X and Y are partners in a firm sharing profits in the ratio of 3:2. They admitted Z as a new partner for 1/4 share. The new profit sharing ratio between X and Y will be 2:1. Calculate their sacrificing ratio.

• A. 2:3
• B. 3:2
• C. 1:2
• D. 2:1

Hint:

Sacrifice is old share minus new share. Find new shares from the 3/4 left after Z's share.

Answer 1

The Correct Option is A

Step 1: Approach:
Work with a total of 20 parts so that all shares are whole numbers.

Step 2: Old shares in 20 parts:
X = 3/5 of 20 = 12 parts. Y = 2/5 of 20 = 8 parts.

Step 3: New shares in 20 parts:
Z takes 1/4 of 20 = 5 parts. The remaining 15 parts go to X and Y in the ratio 2:1, so X = 10 parts and Y = 5 parts.

Step 4: Compare:
X gives up 12 - 10 = 2 parts. Y gives up 8 - 5 = 3 parts. Check: 2 + 3 = 5, which equals Z's share.

Step 5: Read the result:
Sacrifice ratio is 2:3. This is option 1.

Final Answer:
Sacrificing ratio is 2:3. \[ \boxed{2:3} \]