Question

M and N share profits in the ratio of 3:1. They admit O for 1/4th share. O acquires his share entirely from M.
The new profit-sharing ratio of M, N and O will be:

• A. 8 : 3 : 1
• B. 2 : 1 : 1
• C. 5 : 3 : 2
• D. 3 : 2 : 1

Hint:

When a new partner acquires their share entirely from one partner, simply subtract that share directly from the sacrificing partner's old share.
Leave the non-sacrificing partner's share untouched.
Express all shares with the same denominator to instantly find the new profit-sharing ratio.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question requires us to calculate the new profit-sharing ratio of partners M, N, and O.
The old profit-sharing ratio of M and N is 3:1.
The new partner, O, is admitted for a 1/4th share of the profits.
The critical condition is that O acquires his entire share of profits from partner M.
This means only M sacrifices a portion of his profit share, while N's profit share remains unchanged.

Step 2: Key Formula or Approach:
1. Identify the old shares of the partners:
\[ \text{M's Old Share} = \frac{3}{4}, \quad \text{N's Old Share} = \frac{1}{4} \]
2. Deduct the sacrificed share from the partner who is surrendering their share:
\[ \text{New Share} = \text{Old Share} - \text{Sacrifice} \]
3. Express the new shares of all partners with a common denominator to find the new ratio.

Step 3: Detailed Explanation:
1. We start by noting the old profit shares of M and N.
Since the old ratio is 3:1, the shares are:
\[ \text{M's Old Share} = \frac{3}{4} \]
\[ \text{N's Old Share} = \frac{1}{4} \]
2. O is admitted with a 1/4th share of profits.
The problem states that O acquires his share entirely from M.
Therefore, M's sacrifice is \(\frac{1}{4}\), and N's sacrifice is \(0\).
3. Now, we calculate the new shares of the partners:
For M:
\[ \text{M's New Share} = \text{Old Share} - \text{Sacrifice} = \frac{3}{4} - \frac{1}{4} = \frac{2}{4} \]
For N:
Since N does not make any sacrifice, his share remains the same as his old share:
\[ \text{N's New Share} = \frac{1}{4} \]
For O:
O's share is explicitly given as:
\[ \text{O's Share} = \frac{1}{4} \]
4. We combine the new shares of M, N, and O to find their ratio:
\[ \text{New Ratio} = \text{M's Share} : \text{N's Share} : \text{O's Share} \]
\[ \text{New Ratio} = \frac{2}{4} : \frac{1}{4} : \frac{1}{4} \]
\[ \text{New Ratio} = 2 : 1 : 1 \]
This shows that only M's share is reduced, while N's share remains untouched.

Step 4: Final Answer:
The new profit-sharing ratio of M, N, and O is 2:1:1.
Thus, Option (B) is the correct answer.