Question

The cost of a car depreciates every year by 25%. If the
present cost of car is 8 lakhs, then find the cost of the
car after 2 years.​

Answer 1

Given :-

• The cost of a car depreciates every year by 25%.  
• The present cost of car is 8 lakhs

To Find :-  

• Find the cost of the car after 2 years.

Solution :-  

~Here, we’re given the present cost of car and it’s rate of depreciation for 2 years. To Find it’s age after the given time we can apply the amount formula but we’ll not add the rate percent but we need to subtract it as the cost is decreasing every year.  

_____________

As we know that ,

$\bf \maltese \;\; A = P \bigg\{ 1 + \dfrac{r}{100} \bigg\}^{n}$

Where,  

• A is the amount  
• P is the principal amount  
• R is the rate percent  
• N is the time

But for this question the formula will be :  

$\bf \maltese \;\; A = P \bigg\{ 1 - \dfrac{r}{100} \bigg\}^{n}$

________________

Finding the cost of car after 2 years :-

$\sf \implies A = 8,00,000 \bigg\{ 1 - \dfrac{25}{100} \bigg\}^{2}$ 

$\sf \implies A = 8,00,000 \bigg\{ \dfrac{100-25}{100} \bigg\}^{2}$

$\sf \implies A = 8,00,000 \bigg\{ \dfrac{75}{100} \bigg\}^{2}$  

$\sf \implies A = 8,00,000 \times \dfrac{75}{100} \times \dfrac{75}{100}$ 

$\sf \implies A = 80 \times 75 \times 75$  

$\sf \leadsto A = Rs. \; 4,50,000$

________________  

Hence,  

• The amount of car after 2 years will be Rs. 4,50,000

 

_________________

Answer 2

Step-by-step explanation:

The cost of a car depreciates every year by 25%.

The present cost of car is 8 lakhs

To Find :-

Find the cost of the car after 2 years.

Solution :-

~Here, we’re given the present cost of car and it’s rate of depreciation for 2 years. To Find it’s age after the given time we can apply the amount formula but we’ll not add the rate percent but we need to subtract it as the cost is decreasing every year.

_____________

As we know that ,

\bf \maltese \;\; A = P \bigg\{ 1 + \dfrac{r}{100} \bigg\}^{n}✠A=P{1+

100

r

}

n

Where,

A is the amount

P is the principal amount

R is the rate percent

N is the time

But for this question the formula will be :

\bf \maltese \;\; A = P \bigg\{ 1 - \dfrac{r}{100} \bigg\}^{n}✠A=P{1−

100

r

}

n

________________

Finding the cost of car after 2 years :

\sf \implies A = 8,00,000 \bigg\{ 1 - \dfrac{25}{100} \bigg\}^{2}⟹A=8,00,000{1−

100

25

}

2

\sf \implies A = 8,00,000 \bigg\{ \dfrac{100-25}{100} \bigg\}^{2}⟹A=8,00,000{

100

100−25

}

2

\sf \implies A = 8,00,000 \bigg\{ \dfrac{75}{100} \bigg\}^{2}⟹A=8,00,000{

100

75

}

2

\sf \implies A = 8,00,000 \times \dfrac{75}{100} \times \dfrac{75}{100}⟹A=8,00,000×

100

75

×

100

75

\sf \implies A = 80 \times 75 \times 75⟹A=80×75×75

\sf \leadsto A = Rs. \; 4,50,000⇝A=Rs.4,50,000

________________

Hence,

The amount of car after 2 years will be Rs. 4,50,000