A and B invested Rs. 2000 and Rs. (2000 +x) respectively . B withdraw from the business after 8 months .If at the end of the year profits obtained by B is 20% less than the profit obtained by A then find the value of x

Options

A. A)Rs. 500
B. B)Rs. 400
C. C)Rs. 450
D. D)Rs. 600

Answer

To solve the problem step by step, we will follow the given information about the investments made by A and B, their respective time periods, and the relationship between their profits.

### Step 1: Identify the Investments and Time Periods
- A invests Rs. 2000 for 12 months.
- B invests Rs. (2000 + x) for 8 months.

### Step 2: Calculate the Profit Ratios
The profit earned by each partner can be calculated using the formula:
\[ \text{Profit} = \text{Investment} \times \text{Time} \]

For A:
\[ \text{Profit of A} = 2000 \times 12 = 24000 \]

For B:
\[ \text{Profit of B} = (2000 + x) \times 8 \]

### Step 3: Set Up the Equation Based on Profit Relationship
According to the problem, the profit obtained by B is 20% less than the profit obtained by A. This can be expressed as:
\[ \text{Profit of B} = \text{Profit of A} - 0.2 \times \text{Profit of A} \]
\[ \text{Profit of B} = 0.8 \times \text{Profit of A} \]

Substituting the profit of A:
\[ \text{Profit of B} = 0.8 \times 24000 = 19200 \]

### Step 4: Set Up the Equation
Now we can set up the equation for B's profit:
\[ (2000 + x) \times 8 = 19200 \]

### Step 5: Solve for x
Now, we will simplify and solve for x:
1. Divide both sides by 8:
\[ 2000 + x = \frac{19200}{8} \]
\[ 2000 + x = 2400 \]

2. Subtract 2000 from both sides:
\[ x = 2400 - 2000 \]
\[ x = 400 \]

### Conclusion
The value of x is Rs. 400.