Hint: The value of the machine 2 years ago will be greater than the present value. Take the value as ‘x’. Thus find the rate for 2 years and equate it to present value find x.
Depreciation is the reduction in the value of an asset that gets older or as wear and tear occurs or the decline of one currency in relation to another.
Now it is said that the machine depreciates at a rate of 10% per annum. This may be because of the machine getting older and less valuable and useful because of its age and wear and tear. Now this happens because of depreciation. This can also mean the reduction of the purchasing value of money.
We have been given the present value of the machine as Rs.162, 000.
We need to find the value of the machine 2 years ago. So let us consider the value of the machine 2 years ago as ‘x’.
The machine depreciates 10% per year. Thus the rate can be taken for 1 year as (100 - 10)% = 90%.
Thus the value of machine 2 year ago =\[x\times \dfrac{90}{100}\times \dfrac{90}{100}\]
i.e. we can say that,
\[\begin{align}
& \dfrac{x\times 90\times 90}{100\times 100}=162000 \\
& \therefore x=\dfrac{162000\times 100\times 100}{90\times 90}=200000 \\
\end{align}\]
Thus we can say that the value of money 2 years ago was Rs.2, 00, 000.
\[\therefore \] Option (c) is the correct answer.
Note: We can also find the amount by adding the depreciated value.
Present value = Rs.162000
Value of 1 year ago = Present value + 10% depreciation of Present value.
\[=162000+\dfrac{10}{100}\times 162000\]
\[=162000+16200\] = Rs.178200
Value 2 years ago = Value of 1 year ago + 10% depreciation of value 1 year ago
\[\begin{align}
& =178200+\dfrac{10}{100}\times 178200 \\
& =178200+17820=196020 \\
\end{align}\]
This amount is Rs.196020, which we can approximate to Rs.2, 00, 000.
