A and B entered into a partnership with amount Rs 2500 and Rs 4500 respectively and C joined them after 5 months with amount rs 2400 and if total profit at the end of the year is Rs 16800, then find the difference between profit amount earned by B and C? (in Rs)

Options

A. A)6000
B. B)5800
C. C)5600
D. D)6200

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Determine the investments of A, B, and C
- A invests Rs 2500
- B invests Rs 4500
- C invests Rs 2400

### Step 2: Calculate the ratio of their investments
To simplify the calculations, we can divide each investment by 100:
- A's investment: 2500 / 100 = 25
- B's investment: 4500 / 100 = 45
- C's investment: 2400 / 100 = 24

Thus, the ratio of their investments is:
\[ A : B : C = 25 : 45 : 24 \]

### Step 3: Determine the time of investment for each partner
- A and B invest for the entire year (12 months).
- C joins after 5 months, so C invests for 7 months.

### Step 4: Calculate the effective investment time for each partner
Now, we calculate the effective investment for each partner by multiplying their investment by the time they invested:
- A's effective investment: \( 25 \times 12 = 300 \)
- B's effective investment: \( 45 \times 12 = 540 \)
- C's effective investment: \( 24 \times 7 = 168 \)

### Step 5: Find the total effective investment
Now, we sum up the effective investments:
\[ 300 + 540 + 168 = 1008 \]

### Step 6: Calculate the profit share ratio
The profit share ratio is:
\[ A : B : C = 300 : 540 : 168 \]

### Step 7: Simplify the ratio
To simplify, we can divide each term by 12:
- A: \( 300 / 12 = 25 \)
- B: \( 540 / 12 = 45 \)
- C: \( 168 / 12 = 14 \)

Thus, the simplified ratio is:
\[ A : B : C = 25 : 45 : 14 \]

### Step 8: Calculate the total parts in the ratio
Total parts = \( 25 + 45 + 14 = 84 \)

### Step 9: Determine the value of each part
Given that the total profit is Rs 16800, we can find the value of one part:
\[ \text{Value of 1 part} = \frac{16800}{84} = 200 \]

### Step 10: Calculate the profit for B and C
Now we can calculate the profit for B and C:
- Profit for B: \( 45 \times 200 = 9000 \)
- Profit for C: \( 14 \times 200 = 2800 \)

### Step 11: Find the difference between the profits of B and C
The difference in profit between B and C is:
\[ 9000 - 2800 = 6200 \]

### Final Answer
The difference between the profit amount earned by B and C is Rs 6200.

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