Question

The cost price of a car is \[Rs.4,00,000\]. If its price decreases by 10% every year, then when will the car cost after 3 years?
a) \[Rs.3,00,000\]
b) \[Rs.2,91,700\]
c) \[Rs.2,91,600\]
d) \[Rs.2,50,000\]

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 the 10% of 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 \[Rs.4,00,000\]
First calculating 10% of 400,000 so, it will be
$\Rightarrow$ \[400000 \times \dfrac{{10}}{{100}} = 40000\]
Nor, cost price after one year will be decreased by 10% and so that the amount will be $\Rightarrow$ \[400000 - 40000 = 360000\]
Now, the depreciated value of a car after one year is \[Rs.3,60,000\].
At the end of the second year again 10% of its value is depreciated, which will be \[\begin{array}{l} = 360000 - 360000\left( {\dfrac{{10}}{{100}}} \right)\\ = 360000 - 36000\\ = 324000\end{array}\]
Now, depreciated value of car after two year will be
\[\begin{array}{l} = 324000 - 324000\left( {\dfrac{{10}}{{100}}} \right)\\ = 324000 - 32400\\ = 291600\end{array}\]
Correct answer is option (c).

Note: In mathematics, a percentage is a number or ratio that represents a fraction of 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
\[\begin{array}{l}y \to 100.\\? \to \left( x \right)\end{array}\]