The value of a machine decreases every year at the rate of 5%. If its present value is Rs. 411540, what was its value before 3 years ago?

Options

A. 450000
B. 460000
C. 475000
D. 480000

Answer

To find the value of the machine before 3 years ago, we can use the formula for depreciation. The value of the machine decreases by 5% each year. This means that after each year, the machine retains 95% of its value.

Let's denote the value of the machine 3 years ago as \( x \).

### Step 1: Write the formula for depreciation
The value of the machine after 1 year can be expressed as:
\[ \text{Value after 1 year} = x \times \left(1 - \frac{5}{100}\right) = x \times 0.95 \]

After 2 years, the value will be:
\[ \text{Value after 2 years} = x \times 0.95 \times 0.95 = x \times (0.95)^2 \]

After 3 years, the value will be:
\[ \text{Value after 3 years} = x \times (0.95)^3 \]

### Step 2: Set up the equation
We know that the present value of the machine is Rs. 411540. Therefore, we can set up the equation:
\[ x \times (0.95)^3 = 411540 \]

### Step 3: Calculate \( (0.95)^3 \)
Now we will calculate \( (0.95)^3 \):
\[ (0.95)^3 = 0.857375 \]

### Step 4: Substitute and solve for \( x \)
Now substitute \( (0.95)^3 \) into the equation:
\[ x \times 0.857375 = 411540 \]
To find \( x \), divide both sides by \( 0.857375 \):
\[ x = \frac{411540}{0.857375} \]

### Step 5: Perform the division
Now, we will calculate the value:
\[ x \approx 480000 \]

### Conclusion
Thus, the value of the machine before 3 years ago was approximately Rs. 480000.