Find the gross value of an Estate which yield Rs.3800 after a commission of `5%` has been deducted

Options

A. 3900
B. 4000
C. 4100
D. 3610

Answer

To find the gross value of an estate that yields Rs. 3800 after a 5% commission has been deducted, we can follow these steps:

### Step 1: Define the Gross Value
Let the gross value of the estate be represented as \( x \).

### Step 2: Calculate the Deduction
The commission deducted is 5% of the gross value. Therefore, the deduction can be expressed as:
\[ \text{Deduction} = \frac{5}{100} \times x = 0.05x \]

### Step 3: Calculate the Remaining Value After Deduction
The remaining value after the deduction is the gross value minus the deduction:
\[ \text{Remaining Value} = x - 0.05x = 0.95x \]

### Step 4: Set Up the Equation
According to the problem, the remaining value after the commission has been deducted is Rs. 3800. Therefore, we can set up the equation:
\[ 0.95x = 3800 \]

### Step 5: Solve for Gross Value
To find \( x \), we can rearrange the equation:
\[ x = \frac{3800}{0.95} \]

### Step 6: Calculate the Value
Now, we can perform the calculation:
\[ x = \frac{3800 \times 100}{95} = \frac{380000}{95} \]
Calculating this gives:
\[ x = 4000 \]

### Conclusion
Thus, the gross value of the estate is Rs. 4000.

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