Mr. A starts a business with an investment of Rs. 28,000. Mr. B joins the business after 5 months, After 2 more months Mr. C joins. If the ratio of their profit after one year is 4:2:3, then find out the investments made by Mr. B and Mr. C in rupees? Options are (a) Rs. 20,000, Rs. 30,000 (b) Rs. 50,000, Rs. 20,000 (c) Rs. 12,000, Rs. 25,200 (d) Rs. 24000, Rs. 50,400.

Options

A. Rs. 20,000, Rs. 30,000
B. Rs. 50,000, Rs. 20,000
C. Rs. 12,000, Rs. 25,200
D. Rs. 24000, Rs. 50,400

Answer

To solve the problem, we need to find the investments made by Mr. B and Mr. C based on the profit-sharing ratio after one year. Let's break it down step by step.

### Step 1: Understand the time of investment
- Mr. A invests Rs. 28,000 for 12 months (1 year).
- Mr. B joins after 5 months, so he invests for 7 months.
- Mr. C joins after 2 more months, which means he joins after 7 months. Therefore, he invests for 5 months.

### Step 2: Set up the profit-sharing ratio
The profit-sharing ratio is given as 4:2:3 for Mr. A, Mr. B, and Mr. C respectively.

### Step 3: Calculate the effective capital for each partner
The profit is distributed based on the product of capital and time invested.

- For Mr. A:
\[ \text{Effective Capital of A} = 28000 \times 12 = 336000 \]

- For Mr. B (let's denote his investment as \( x \)):
\[ \text{Effective Capital of B} = x \times 7 \]

- For Mr. C (let's denote his investment as \( y \)):
\[ \text{Effective Capital of C} = y \times 5 \]

### Step 4: Set up the equations based on the profit ratio
From the profit-sharing ratio, we can write:
\[ \frac{336000}{x \times 7} = \frac{4}{2} \quad \text{(for A and B)} \]
\[ \frac{336000}{y \times 5} = \frac{4}{3} \quad \text{(for A and C)} \]

### Step 5: Solve for \( x \) (investment of Mr. B)
From the first equation:
\[ \frac{336000}{x \times 7} = 2 \implies 336000 = 2x \times 7 \implies 336000 = 14x \implies x = \frac{336000}{14} = 24000 \]

### Step 6: Solve for \( y \) (investment of Mr. C)
From the second equation:
\[ \frac{336000}{y \times 5} = \frac{4}{3} \implies 336000 \times 3 = 4y \times 5 \implies 1008000 = 20y \implies y = \frac{1008000}{20} = 50400 \]

### Final Answer
- Investment of Mr. B = Rs. 24,000
- Investment of Mr. C = Rs. 50,400

### Conclusion
Thus, the investments made by Mr. B and Mr. C are Rs. 24,000 and Rs. 50,400 respectively, which corresponds to option (d).

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