In a business A, B and C invested Rs. 380, Rs. 400, and 420 respectively. Divide a net profit of Rs. 180 among the partners.

Answer

To solve the problem of dividing the net profit of Rs. 180 among partners A, B, and C based on their investments, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Investments:**
- A's investment = Rs. 380
- B's investment = Rs. 400
- C's investment = Rs. 420

2. **Calculate the Total Investment:**
\[ \text{Total Investment} = 380 + 400 + 420 = 1200 \]

3. **Determine the Ratio of Investments:**
- The ratio of A's, B's, and C's investments can be simplified as follows:
\[ \text{A : B : C} = 380 : 400 : 420 \]
To simplify, we can divide each term by 20:
\[ = 19 : 20 : 21 \]

4. **Calculate the Total Parts in the Ratio:**
\[ \text{Total Parts} = 19 + 20 + 21 = 60 \]

5. **Calculate Each Partner's Share of the Profit:**
- **A's Share:**
\[ \text{A's Profit} = \left(\frac{19}{60}\right) \times 180 = \frac{3420}{60} = 57 \]

- **B's Share:**
\[ \text{B's Profit} = \left(\frac{20}{60}\right) \times 180 = \frac{3600}{60} = 60 \]

- **C's Share:**
\[ \text{C's Profit} = \left(\frac{21}{60}\right) \times 180 = \frac{3780}{60} = 63 \]

6. **Final Distribution of Profit:**
- A's Profit = Rs. 57
- B's Profit = Rs. 60
- C's Profit = Rs. 63

### Summary of the Solution:
- A receives Rs. 57
- B receives Rs. 60
- C receives Rs. 63