The value of a machine depreciates at the rate of 20 % per annum. If its present value is Rs. 96000, what was the value (in Rs) of the machine 2 years ago ?

Options

A. 138240
B. 134400
C. 15000
D. 144000

Answer

To find the value of the machine 2 years ago, we need to reverse the depreciation process. The machine depreciates at a rate of 20% per annum, which means that every year, the machine retains 80% of its value (100% - 20% = 80%).

Let's denote:
- Present Value (PV) = Rs. 96,000
- Depreciation Rate = 20% per annum
- Value 2 years ago = X

### Step 1: Calculate the value of the machine after 1 year
The value of the machine after 1 year can be calculated using the formula:
\[ \text{Value after 1 year} = \text{Present Value} \div (1 - \text{Depreciation Rate}) \]
Here, the depreciation rate is 20%, so we can express it as 0.20.

So, the value after 1 year:
\[ \text{Value after 1 year} = 96000 \div 0.8 = 120000 \]

### Step 2: Calculate the value of the machine 2 years ago
Now, we will apply the same formula to find the value 2 years ago. We will take the value after 1 year and divide it by the same factor (0.8) to find the value 2 years ago.

\[ \text{Value 2 years ago} = \text{Value after 1 year} \div 0.8 \]
Substituting the value we just calculated:
\[ \text{Value 2 years ago} = 120000 \div 0.8 = 150000 \]

### Conclusion
Thus, the value of the machine 2 years ago was Rs. 150,000.

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