A , B and C start a business with investment of ? 50000 each. A remains in partnership for 9 month, B for 6 months and C for 12 months. Then, find the ratio of their profits.

Answer

To find the ratio of profits among A, B, and C based on their investments and the time they remained in the business, we can follow these steps:

### Step 1: Identify the investments and time periods
- A, B, and C each invested ₹50,000.
- A remained in the business for 9 months.
- B remained in the business for 6 months.
- C remained in the business for 12 months.

### Step 2: Calculate the effective capital contribution
The effective capital contribution can be calculated by multiplying the investment by the time period for which each partner stayed in the business.

- For A:
\[ \text{Effective Capital of A} = \text{Investment} \times \text{Time} = 50,000 \times 9 = 450,000 \]

- For B:
\[ \text{Effective Capital of B} = \text{Investment} \times \text{Time} = 50,000 \times 6 = 300,000 \]

- For C:
\[ \text{Effective Capital of C} = \text{Investment} \times \text{Time} = 50,000 \times 12 = 600,000 \]

### Step 3: Write down the effective capital contributions
- Effective Capital of A = ₹450,000
- Effective Capital of B = ₹300,000
- Effective Capital of C = ₹600,000

### Step 4: Find the ratio of their effective capital contributions
Now, we can express the effective capital contributions in ratio form:
\[ \text{Ratio of A : B : C} = 450,000 : 300,000 : 600,000 \]

### Step 5: Simplify the ratio
To simplify the ratio, we can divide each term by 150,000:
\[ \frac{450,000}{150,000} : \frac{300,000}{150,000} : \frac{600,000}{150,000} = 3 : 2 : 4 \]

### Final Result
Thus, the ratio of their profits is:
\[ \text{A : B : C} = 3 : 2 : 4 \]

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