Question

14. The value of a car depreciates 20% every year. If
after two years, the price of a car is 420000,
find the original price of the car?
​

Answer 1

Answer:

656250

Step-by-step explanation:

(x-20x/100) - (x-20x/100)×20/100 = 420000

Answer 2

Answer :-

Rs.656250

Explanation :-

Given :

Value of car depreciates 20% every year.

Price of car after two years = 420000

Time = 2 years

To Find :

Original price = ?

Solution :

Let the original price be “x”

We know,

$\sf{}A=P\bigg(1-\dfrac{r}{100}\bigg)^n$

Where,

A is the amount after two years

r is the rate of depreciation every year,

P is x and n is the time period.

Put their find “x”

$\rm{}:\implies 420000=x\bigg(1-\dfrac{20}{100}\bigg)^2$

$\rm{}:\implies 420000=x\bigg(\dfrac{1\times 100-20\times 1}{100}\bigg)^2$

$\rm{}:\implies 420000=x\bigg(\dfrac{100-20}{100}\bigg)^2$

$\rm{}:\implies 420000=x\bigg(\dfrac{80}{100}\bigg)^2$

$\rm{}:\implies 420000=x\times\dfrac{6400}{10000}$

$\rm{}:\implies 420000=x\times\dfrac{64}{100}$

$\rm{}:\implies 420000=x\times\dfrac{32}{50}$

$\rm{}:\implies 420000=x\times\dfrac{16}{25}$

$\rm{}:\implies 420000\div\dfrac{16}{25}=x$

$\rm{}:\implies 420000\times \dfrac{25}{16}=x$

$\rm{}:\implies x=210000\times \dfrac{16}{8}$

$\rm{}:\implies x=105000\times \dfrac{25}{4}$

$\rm{}:\implies x=52500\times \dfrac{25}{2}$

$\rm{}:\implies x=26250\times \dfrac{25}{1}$

$\rm{}\therefore x=Rs.656250$

Therefore,original price of the car is equal to Rs.656250