A and B started a business. B's investment was 2.5 times that of A. The ratio of the time period for which A invested to that for which B invested was 3 : 1. If the total investment made by A and B together was 28000 and the annual profit earned. was 2500 less than A's investment, then what was the difference between A's share and B's share in the annual profit?

Options

A. RS... 200
B. RS... 800
C. RS... 500
D. RS... 400

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Investments
Let A's investment be \( x \). Then, B's investment, being 2.5 times that of A, will be:
\[ B = 2.5x \]

### Step 2: Total Investment
According to the problem, the total investment made by A and B together is 28000. Therefore, we can write:
\[ x + 2.5x = 28000 \]
This simplifies to:
\[ 3.5x = 28000 \]

### Step 3: Solve for A's Investment
To find \( x \), divide both sides by 3.5:
\[ x = \frac{28000}{3.5} \]
Calculating this gives:
\[ x = 8000 \]
Thus, A's investment is \( 8000 \) and B's investment is:
\[ B = 2.5 \times 8000 = 20000 \]

### Step 4: Time Periods of Investment
The ratio of the time period for which A invested to that for which B invested is given as 3:1. Let A's time period be \( 3t \) and B's time period be \( t \).

### Step 5: Calculate Profit Sharing Ratio
The profit sharing ratio is determined by the product of investment and time.

For A:
\[ \text{A's share} = \text{Investment of A} \times \text{Time of A} = 8000 \times 3t = 24000t \]

For B:
\[ \text{B's share} = \text{Investment of B} \times \text{Time of B} = 20000 \times t = 20000t \]

### Step 6: Total Profit Calculation
The total profit can be calculated as:
\[ \text{Total Profit} = \text{A's share} + \text{B's share} = 24000t + 20000t = 44000t \]

### Step 7: Annual Profit Relation
According to the problem, the annual profit earned was 2500 less than A's investment:
\[ \text{Total Profit} = 8000 - 2500 = 5500 \]

### Step 8: Set Up the Equation
Equating the total profit expressions:
\[ 44000t = 5500 \]
Solving for \( t \):
\[ t = \frac{5500}{44000} = \frac{1}{8} \]

### Step 9: Calculate Individual Shares of Profit
Now, substituting \( t \) back to find A's and B's shares:
- A's share:
\[ \text{A's Profit} = 24000t = 24000 \times \frac{1}{8} = 3000 \]
- B's share:
\[ \text{B's Profit} = 20000t = 20000 \times \frac{1}{8} = 2500 \]

### Step 10: Find the Difference in Profit Shares
The difference between A's share and B's share in the annual profit is:
\[ \text{Difference} = \text{A's Profit} - \text{B's Profit} = 3000 - 2500 = 500 \]

### Final Answer
The difference between A's share and B's share in the annual profit is:
\[ \boxed{500} \]