Question

The value of a machine depreciates at a rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was
1) Rs. 10000
2) Rs. 11372
3) Rs. 12000
4) Rs. 12500

Answer 1

Hint: We will use the formula \[{\text{Final price}} = {\text{initial price}}{\left( {1 + \dfrac{{{\text{rate}}}}{{100}}} \right)^{{\text{time}}}}\] to find the initial price of the machine and rest of the things are given in the question. The rate is depreciating so we will take \[ - 10\% \]. After this we will simplify the expression to get the purchase price.

Complete step-by-step answer:
Consider the given data from the question,
Here, we have \[{\text{Final price}} = Rs.8748\], \[{\text{Time}} = 3yrs\] and the rate is getting depreciated at 10% of every year.
Since, we know the formula,
\[{\text{Final price}} = {\text{initial price}}{\left( {1 + \dfrac{{{\text{rate}}}}{{100}}} \right)^{{\text{time}}}}\]
Thus, we will let the value of the initial price as \[x\] and as the rate is getting depreciated so, we will use \[ - 10\% \] per annum.
Hence, substitute the values in the formula to evaluate the value of initial price,
We get,
\[ \Rightarrow 8748 = x{\left( {1 - \dfrac{{{\text{10}}}}{{100}}} \right)^{\text{3}}}\]
Further, simplifying the obtained expression, we get,
\[
   \Rightarrow x{\left( {\dfrac{{90}}{{100}}} \right)^3} = 8748 \\
   \Rightarrow x \times \dfrac{9}{{10}} \times \dfrac{9}{{10}} \times \dfrac{9}{{10}} = 8748 \\
   \Rightarrow x = 8748 \times \dfrac{{10}}{9} \times \dfrac{{10}}{9} \times \dfrac{{10}}{9} \\
   \Rightarrow x = 12000 \\
\]
Thus, from this, we get the initial price value of the machine as Rs. 12000.
Hence, option C is correct.

Note: The value of rate is negative as the rate is getting depreciating at the rate of 10% every year. Direct apply the formula \[{\text{Final price}} = {\text{initial price}}{\left( {1 + \dfrac{{{\text{rate}}}}{{100}}} \right)^{{\text{time}}}}\] to know the initial price of the value of a machine.