Question

Grace bought a new van for Rs. 15000. Each year, the value of her car depreciated by 10%. Calculate the value of the car before 2 years.
a) 12150
b) 22150
c) 32150
d) 42150

Answer 1

Hint: To calculate the value of car, before 2 years, we should know that depreciation can be calculated using its formula, which is \[A=P{{\left( 1-\dfrac{r}{100} \right)}^{n}}\], where P represents initial principal balance, r represents the rate of depreciation, n represent the number of depreciation.

Complete step-by-step answer:
In this question, we have been given that Grace bought a new van for Rs. 15000. Each year, the value of a car depreciates by 10%. We have to find the value of a car before 2 years.
We know that, the depreciation of a value object can be calculated by using the formula \[A=P{{\left( 1-\dfrac{r}{100} \right)}^{n}}\], where P represents the initial principal balance of the object, r represents the rate of depreciation of the object, n represents the number of times depreciation took place.
So, according to the question, we can see that, P = Rs. 15000, r = 10% and n = 2 years.
So, \[A=\left( 15000 \right){{\left( 1-\dfrac{10}{100} \right)}^{2}}\], where A represents the value of car before 2 years.
\[\Rightarrow A=\left( 15000 \right){{\left( \dfrac{100-10}{100} \right)}^{2}}\]
Now, we will simplify it further to obtain the value of the car.
So, \[A=\left( 15000 \right){{\left( \dfrac{90}{100} \right)}^{2}}\]
\[\Rightarrow A=\left( 15000 \right){{\left( \dfrac{9}{10} \right)}^{2}}\]
\[\Rightarrow A=\left( 15000 \right)\left( \dfrac{81}{100} \right)\]
\[\Rightarrow A=\left( 150 \right)\left( 81 \right)\]
\[\Rightarrow A=12150\]
So, the value of the car before 2 years will be Rs. 12150.
Hence, option (a) is correct.

Note: In the question, before 2 years means the depreciation on the value of the car before completion of the time period of 2 years. Also, we can find the value of a car by subtracting the 10% of the value of the car and then by subtracting the 10% of the obtained value.