If the value of a machine depreciates by 10% of its value at the beginning of the year and its present value is estimated as Rs. 10935, then its value 3 yr ago was

Options

A. Rs. 15000
B. Rs. 12000
C. Rs. 11000
D. None of these

Answer

To find the value of the machine 3 years ago, we will follow these steps:

### Step 1: Define the present value and depreciation
Let the value of the machine 3 years ago be represented as \( 100x \). Since the machine depreciates by 10% at the beginning of each year, we can express the value of the machine for each subsequent year.

### Step 2: Calculate the value after 1 year
After the first year, the value of the machine will be:
\[ \text{Value after 1 year} = 100x - 10\% \text{ of } 100x = 100x - 10x = 90x \]

### Step 3: Calculate the value after 2 years
After the second year, the value of the machine will be:
\[ \text{Value after 2 years} = 90x - 10\% \text{ of } 90x = 90x - 9x = 81x \]

### Step 4: Calculate the value after 3 years
After the third year, the value of the machine will be:
\[ \text{Value after 3 years} = 81x - 10\% \text{ of } 81x = 81x - 8.1x = 72.9x \]

### Step 5: Set up the equation with the present value
We know that the present value of the machine is Rs. 10,935. Therefore, we can set up the equation:
\[ 72.9x = 10935 \]

### Step 6: Solve for \( x \)
To find \( x \), we divide both sides by 72.9:
\[ x = \frac{10935}{72.9} \approx 150 \]

### Step 7: Calculate the value 3 years ago
Now that we have \( x \), we can find the value of the machine 3 years ago:
\[ \text{Value 3 years ago} = 100x = 100 \times 150 = 15000 \]

### Conclusion
Thus, the value of the machine 3 years ago was Rs. 15,000.

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