A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years?

Options

A. 10 : 10 : 9
B. 20:20:19
C. 20:19:18
D. 19: 19:18

Answer

To solve the problem of how A, B, and C should divide the profits at the end of 3 years based on their investments, we will follow these steps:

### Step 1: Calculate A's Contribution
- A initially invests Rs. 25 lakhs for 3 years.
- After 1 year, A adds another Rs. 10 lakhs, making the total investment Rs. 35 lakhs for the remaining 2 years.

**Calculation:**
- For the first year: \( 25 \text{ lakhs} \times 1 \text{ year} = 25 \text{ lakhs-years} \)
- For the next two years: \( 35 \text{ lakhs} \times 2 \text{ years} = 70 \text{ lakhs-years} \)

**Total contribution of A:**
\[ 25 + 70 = 95 \text{ lakhs-years} \]

### Step 2: Calculate B's Contribution
- B initially invests Rs. 35 lakhs for 2 years.
- After 2 years, B withdraws Rs. 10 lakhs, so for the last year, B has Rs. 25 lakhs.

**Calculation:**
- For the first two years: \( 35 \text{ lakhs} \times 2 \text{ years} = 70 \text{ lakhs-years} \)
- For the last year: \( 25 \text{ lakhs} \times 1 \text{ year} = 25 \text{ lakhs-years} \)

**Total contribution of B:**
\[ 70 + 25 = 95 \text{ lakhs-years} \]

### Step 3: Calculate C's Contribution
- C invests Rs. 30 lakhs for the entire 3 years.

**Calculation:**
- For 3 years: \( 30 \text{ lakhs} \times 3 \text{ years} = 90 \text{ lakhs-years} \)

**Total contribution of C:**
\[ 90 \text{ lakhs-years} \]

### Step 4: Determine the Ratio of Contributions
Now we have the total contributions in lakhs-years:
- A: 95 lakhs-years
- B: 95 lakhs-years
- C: 90 lakhs-years

**Ratio of contributions:**
\[ A : B : C = 95 : 95 : 90 \]

To simplify this ratio, we can divide all parts by 5:
\[ = 19 : 19 : 18 \]

### Final Answer
The profits should be divided in the ratio of **19 : 19 : 18**.

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