A,B and C invest in a partnership in ratio `5:3:7` and investment of A is Rs . 200 less than investment of C. Partner B invests for `1/5` th and A and C invest for `1/12 th and 1/15 th` respectively of total time of investment . If profit of B is Rs.800 more than that of C than find profit of A.

Options

A. A)Rs 1000
B. B)Rs 2500
C. C)Rs 2800
D. D)Rs 1400

Answer

To solve the problem step by step, we will follow the given information and calculate the required values.

### Step 1: Define the Investments
Let the investments of A, B, and C be represented as:
- A's investment = 5x
- B's investment = 3x
- C's investment = 7x

According to the problem, A's investment is Rs. 200 less than C's investment:
\[ 5x = 7x - 200 \]

### Step 2: Solve for x
Rearranging the equation:
\[ 7x - 5x = 200 \]
\[ 2x = 200 \]
\[ x = 100 \]

### Step 3: Calculate Individual Investments
Now we can find the actual investments:
- A's investment = \( 5x = 5 \times 100 = 500 \) Rs.
- B's investment = \( 3x = 3 \times 100 = 300 \) Rs.
- C's investment = \( 7x = 7 \times 100 = 700 \) Rs.

### Step 4: Define the Time of Investment
According to the problem, the time of investment for each partner is:
- A invests for \( \frac{1}{12} \) of the total time.
- B invests for \( \frac{1}{5} \) of the total time.
- C invests for \( \frac{1}{15} \) of the total time.

### Step 5: Convert Time into a Common Ratio
To find a common ratio for the time of investment, we can take the LCM of the denominators (12, 5, and 15):
- LCM(12, 5, 15) = 60

Now we can express the time ratios:
- A's time = \( \frac{60}{12} = 5 \)
- B's time = \( \frac{60}{5} = 12 \)
- C's time = \( \frac{60}{15} = 4 \)

### Step 6: Calculate Profit Ratios
The profit for each partner is proportional to their investment multiplied by the time they invested:
- Profit ratio for A = \( 5 \times 5 = 25 \)
- Profit ratio for B = \( 3 \times 12 = 36 \)
- Profit ratio for C = \( 7 \times 4 = 28 \)

### Step 7: Set Up the Profit Equation
According to the problem, B's profit is Rs. 800 more than C's profit:
Let the profit of C be represented as \( 28k \) (where k is a common multiplier for the profit units).
Then, B's profit can be expressed as:
\[ 36k = 28k + 800 \]

### Step 8: Solve for k
Rearranging the equation:
\[ 36k - 28k = 800 \]
\[ 8k = 800 \]
\[ k = 100 \]

### Step 9: Calculate Individual Profits
Now we can find the profits for each partner:
- Profit of A = \( 25k = 25 \times 100 = 2500 \) Rs.
- Profit of B = \( 36k = 36 \times 100 = 3600 \) Rs.
- Profit of C = \( 28k = 28 \times 100 = 2800 \) Rs.

### Conclusion
Thus, the profit of A is Rs. 2500.