Question

The cost price of a car is \[{\text{Rs}}{\text{.4,00,000}}\]. If the price is decreased by \[10\% \]every year , then when will be the cost of a car after \[{\text{3}}\] years ?
A. \[{\text{Rs3,00,000}}\]
B. \[{\text{Rs2,91,700}}\]
C. \[{\text{Rs2,91,600}}\]
D. \[{\text{Rs2,50,000}}\]

Answer 1

Hint: Firstly, calculate the \[10\% \]of base cost price and subtract it from the cost price so it will be the base price of the car after \[1\]year. And so now, calculate then calculate the \[10\% \] of that base price and subtract that amount from that base cost price. Similarly, proceed for the third year also and finally, the cost price after the third year will be obtained.

Complete step by step answer:

Given the cost price of a car is \[{\text{Rs}}{\text{.4,00,000}}\].
First, calculating \[10\% \] of \[{\text{Rs}}{\text{.4,00,000}}\] so it will be
\[{\text{400000 $\times$ }}\dfrac{{{\text{10}}}}{{{\text{100}}}}{\text{ = 40000}}\]
Now, cost price after one year will be decreased by \[10\% \] and so that amount will be
\[{\text{400000 - 40000 = 360000}}\]
Now, the depreciated value of a car after one year is \[{\text{Rs360000}}\].
At the end of the second year again \[10\% \]of its value is depreciated, which will be
\[
  {\text{ = 360000 - 360000(}}\dfrac{{{\text{10}}}}{{{\text{100}}}}{\text{)}} \\
  {\text{ = 360000 - 36000}} \\
  {\text{ = Rs}}{\text{.324000}} \\
 \]
Now, depreciated value of car in after two year will be \[{\text{Rs}}{\text{.324000}}\] and the value at the end of the third year will be
\[
  {\text{ = 324000 - 324000(}}\dfrac{{{\text{10}}}}{{{\text{100}}}}{\text{)}} \\
  {\text{ = 324000 - 32400}} \\
  {\text{ = Rs}}{\text{.291600}} \\
 \]
Hence, option (c) is our required correct answer.

Note: In mathematics, a percentage is a number or ratio that represents a fraction of \[{\text{100}}\].
Cost Price: The price at which an article is purchased, is called its cost price (C.P.). Car depreciation is the difference between how much your car was worth when you bought it and what it's worth when you sell it. The value of your car goes down over time with the wear and tear of everyday use. We can use the way to calculate the x percentage for any y amount using the unitary concept as
\[
  {\text{y}} \to {\text{100}} \\
  ? \to {\text{(x)}} \\
 \].
Here, calculate properly.