A and B enter into partnership investing Rs 12000 and Rs 16000 respectively. After 8 months c joins them with a capital of Rs 15000 . The share of C in a profit of Rs 45600 after 2 years will be

Options

A. Rs 21200
B. RS 19200
C. Rs 14400
D. Rs 12000

Answer

To solve the problem step by step, we will calculate the share of C in the profit based on the capital invested and the time for which it was invested.

### Step 1: Calculate the investment of A, B, and C in terms of "Capital Months"
- A invests Rs 12,000 for 24 months (2 years).
- B invests Rs 16,000 for 24 months (2 years).
- C joins after 8 months, so he invests Rs 15,000 for 16 months (2 years - 8 months).

**Calculation:**
- A's investment in capital months = 12000 * 24 = 288000
- B's investment in capital months = 16000 * 24 = 384000
- C's investment in capital months = 15000 * 16 = 240000

### Step 2: Find the total capital months for A, B, and C
- Total capital months = A's capital months + B's capital months + C's capital months
- Total capital months = 288000 + 384000 + 240000 = 912000

### Step 3: Calculate the ratio of investments
- The ratio of A's, B's, and C's investments in capital months is:
- A : B : C = 288000 : 384000 : 240000

To simplify, we can divide each term by 48000:
- A : B : C = 6 : 8 : 5

### Step 4: Calculate the share of C in the profit
- Total profit = Rs 45600
- C's share of the profit = (C's ratio / Total ratio) * Total profit
- C's share = (5 / (6 + 8 + 5)) * 45600
- C's share = (5 / 19) * 45600

**Calculation:**
- C's share = (5 / 19) * 45600 = 12000

### Final Answer:
C's share in the profit of Rs 45600 after 2 years is Rs 12000.

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