Question

The value of the machine depreciates at the rate of $10\% $ every year. If its present value is $Rs\,38700$, what was its value one year ago?

Answer 1

Hint: The given question revolves around the topic of depreciation. We are given the rate of depreciation of a machine every year and the present value of the machine. We assume the value of the machine one year ago to be x rupees. Then, we calculate the depreciation according to the percentage given. Then, we subtract it from the value of the machine one year ago and equate it with the present value.

Complete step by step answer:
So, let us assume the value of the machine is x rupees.
Then, the rate of depreciation of the machine every year is given as $10\% $.
So, we calculate the depreciation in a year by calculating $10\% $ of the value of the machine one year ago.
So, we get, depreciation in the machine $ = \dfrac{{10}}{{100}} \times Rs\,x$
Cancelling the common factors in numerator and denominator, we get,
$ = Rs\dfrac{{\,x}}{{10}}$
Now, we can calculate the present value of the machine by deducting the depreciation in the machine from the value of the machine one year ago. So, we get,
$ = Rs\,x - Rs\,\dfrac{x}{{10}}$
Taking LCM of the denominator, we get,
\[ = Rs\,\,\left( {\dfrac{{10x - x}}{{10}}} \right)\]
Simplifying the expression,
\[ = Rs\,\,\dfrac{{9x}}{{10}}\]
Now, we equate this expression with the present value of the machine given to us as $Rs\,38700$. So, we get,
\[ \Rightarrow Rs\,\,\dfrac{{9x}}{{10}} = Rs\,38700\]
Finding the value of x in the equation using transposition method, we get,
\[ \Rightarrow Rs\,\,\dfrac{{9x}}{{10}} = Rs\,38700\]
\[ \Rightarrow x = \,38700 \times \left( {\dfrac{{10}}{9}} \right)\]
Cancelling the common factors in numerator and denominator, we get,
\[ \Rightarrow x = \,4300 \times 10\]
Simplifying the calculations further, we get,
\[ \Rightarrow x = \,43000\]
So, the value of the machine one year ago was $43000$ rupees.

Note:
One must have accuracy in arithmetic so as to solve these types of questions within a limited time frame. We should have a clear understanding of how to find the percentage of a specific number so as to find the depreciation for the goods.