Answer :
Answer:
To determine the new profit-sharing ratio after Dev is admitted to the partnership, we follow these steps:
1. **Understand the initial profit-sharing ratio**:
Mary, Raj, and Kapil share profits and losses in the ratio of 3:2:5.
2. **Understand the share admitted to Dev**:
Dev is admitted for 1/4th share, and this share is given by Mary, Raj, and Kapil in the ratio of 1:1:3.
3. **Calculate Dev's share in terms of the original ratio**:
- Dev's share is 1/4th of the total partnership.
- Total initial ratio sum = 3 + 2 + 5 = 10 parts.
- Dev's share = 1/4 * 10 = 2.5 parts.
- Given ratio for Dev = 1:1:3.
4. **Determine Dev's share in absolute terms**:
- Let's denote the parts as follows:
- Mary's share = 1x
- Raj's share = 1x
- Kapil's share = 3x
- Sum of parts for Dev = 1x + 1x + 3x = 5x
- Therefore, 5x = 2. Share
Answer:
7 : 4 : 9 : 10
Explanation:
To determine the new profit-sharing ratio for Mary, Raj, Kapil, and Dev after Dev is admitted for a 1/4th share, follow these steps:
### Step-by-Step Solution
1. **Determine the Total Profit Share**:
The total profit share is always considered to be 1 or 100%.
2. **Identify Dev's Share**:
Dev is given 1/4th of the total profit. Therefore, Dev's share is:
\[
\text{Dev's Share} = \frac{1}{4} = 0.25
\]
3. **Determine the Remaining Share**:
After giving Dev his share, the remaining profit share to be divided among Mary, Raj, and Kapil is:
\[
\text{Remaining Share} = 1 - \frac{1}{4} = \frac{3}{4} = 0.75
\]
4. **Original Ratios for Mary, Raj, and Kapil**:
The original profit-sharing ratio among Mary, Raj, and Kapil is 3:2:5.
5. **Calculate the Total Original Ratio**:
Sum of the original ratio parts:
\[
\text{Total Original Ratio} = 3 + 2 + 5 = 10
\]
6. **Determine the Individual Shares After Dev's Admission**:
The remaining 3/4 share is distributed among Mary, Raj, and Kapil in the original ratio of 3:2:5.
- **Mary's Share**:
\[
\text{Mary's Share} = \frac{3}{10} \times \frac{3}{4} = \frac{9}{40}
\]
- **Raj's Share**:
\[
\text{Raj's Share} = \frac{2}{10} \times \frac{3}{4} = \frac{6}{40}
\]
- **Kapil's Share**:
\[
\text{Kapil's Share} = \frac{5}{10} \times \frac{3}{4} = \frac{15}{40}
\]
7. **Allocate Dev's Share**:
Dev's share of 1/4th is divided by Mary, Raj, and Kapil in the ratio of 1:1:3.
- **Mary's Contribution to Dev's Share**:
\[
\text{Mary's Contribution} = \frac{1}{5} \times \frac{1}{4} = \frac{1}{20}
\]
- **Raj's Contribution to Dev's Share**:
\[
\text{Raj's Contribution} = \frac{1}{5} \times \frac{1}{4} = \frac{1}{20}
\]
- **Kapil's Contribution to Dev's Share**:
\[
\text{Kapil's Contribution} = \frac{3}{5} \times \frac{1}{4} = \frac{3}{20}
\]
8. **Adjust Individual Shares After Giving Dev's Share**:
Subtract the contributions from Mary, Raj, and Kapil's shares and add to Dev's share:
- **Mary's New Share**:
\[
\text{Mary's New Share} = \frac{9}{40} - \frac{1}{20} = \frac{9}{40} - \frac{2}{40} = \frac{7}{40}
\]
- **Raj's New Share**:
\[
\text{Raj's New Share} = \frac{6}{40} - \frac{1}{20} = \frac{6}{40} - \frac{2}{40} = \frac{4}{40} = \frac{1}{10}
\]
- **Kapil's New Share**:
\[
\text{Kapil's New Share} = \frac{15}{40} - \frac{3}{20} = \frac{15}{40} - \frac{6}{40} = \frac{9}{40}
\]
- **Dev's Share** (Already calculated):
\[
\text{Dev's Share} = \frac{1}{4} = \frac{10}{40}
\]
9. **New Profit-Sharing Ratio**:
Combine all the new shares and simplify the ratio:
- **Mary**: \(\frac{7}{40}\)
- **Raj**: \(\frac{4}{40} = \frac{1}{10}\)
- **Kapil**: \(\frac{9}{40}\)
- **Dev**: \(\frac{10}{40}\)
To express the shares in a simple ratio:
\[
\frac{7}{40} : \frac{4}{40} : \frac{9}{40} : \frac{10}{40} \quad \text{becomes} \quad 7 : 4 : 9 : 10
\]
### Final Answer:
The new profit-sharing ratio among Mary, Raj, Kapil, and Dev is:
\[
7 : 4 : 9 : 10
\]