Question

6. The price of a car is 4,50,000. The value of the car depreciates by 20% in the first year
and after that it depreciates 25% every year. What will be the car's value after 3 years. [4 M]​

Answer 1

Given :

Price of a car :- ₹450000

Value depreciation in first year :- 20%

Value depreciation in second year :- 25%

Value depreciation in third year :- 25%

To find :

Value of the car after 3 years.

Solution :

Let's find the values of the car in first and second user and third year respectively.

Value of car in first year :

${\sf \dashrightarrow 450000 - (20\% \: of \: 450000)}$

${\sf \dashrightarrow 450000 - \bigg( \dfrac{20}{100} \times 450000 \bigg)}$

${\sf \dashrightarrow 450000 \bigg( \dfrac{1}{5} \times 450000 \bigg)}$

${\sf \dashrightarrow 450000 - \bigg( \dfrac{1 \times 450000}{5} \bigg)}$

${\sf \dashrightarrow 450000 - \bigg( \dfrac{450000}{5} \bigg)}$

${\sf \dashrightarrow 450000 - 9000}$

${\sf \dashrightarrow 360000}$

Value of car in second year :

${\sf \dashrightarrow 360000 - (25\% \: of \: 360000)}$

${\sf \dashrightarrow 360000 - \bigg( \dfrac{25}{100} \times 360000 \bigg)}$

${\sf \dashrightarrow 360000 - \bigg( \dfrac{1}{4} \times 360000 \bigg)}$

${\sf \dashrightarrow 360000 - \bigg( \dfrac{1 \times 360000}{4} \bigg)}$

${\sf \dashrightarrow 360000 - \bigg( \dfrac{360000}{4} \bigg)}$

${\sf \dashrightarrow 360000 - 90000}$

${\sf \dashrightarrow 270000}$

Value of car in third year :

${\sf \dashrightarrow 270000 - (25\% \: of \: 270000)}$

${\sf \dashrightarrow 270000 - \bigg( \dfrac{25}{100} \times 270000 \bigg)}$

${\sf \dashrightarrow 270000 - \bigg( \dfrac{1}{4} \times 270000 \bigg)}$

${\sf \dashrightarrow 270000 - \bigg( \dfrac{1 \times 270000}{4} \bigg)}$

${\sf \dashrightarrow 270000 - \bigg( \dfrac{270000}{4} \bigg)}$

${\sf \dashrightarrow 270000 - 67500}$

${\sf \dashrightarrow 202500}$

Hence, the price value of the car after three years is ₹202500.

Answer 2

Question:-

The price of a car is 4,50,000. The value of the car depreciates by 20% in the first year and after that it depreciates 25% every year. What will be the car's value after 3 years.

Required Answer:-

Given:-

• The price of a car is 4,50,000
• The value depreciates by 20% in the first year.
• The value depreciates 25% in second year.
• The value depreciates 25% in second year.

To Find:-

• The value of the car after 3 years.

Solution:-

First, let's see what is "Depreciation"

Depreciation refers to when the value of something goes down over time.

The value of a car is usually decreases in value with time. Therefore its value is said to depreciate.

Now, we have to find the value of the car each year respectively.

• Value depreciation on 1st year is by 20%

Value of the car in 1st year:-

=> 4,50,000 - (20% of 4,50,00)

=> 4,50,000 - (20/100 × 4,50,00)

=> 4,50,000 - 90,000

=> 3,60,000

Hence, the value of the car after 1st year is Rs. 3,60,000

Again,

• Value depreciation on 2nd year is 25%

Value of the car in 2nd year:-

=> 3,60,000 - (25% of 3,60,00)

=> 3,60,000 - (25/100 × 3,60,00)

=> 3,60,000 - 90,000

=> 2,70,000

Hence, the value of the car after 2nd year is Rs. 2,70,000

Now,

• Value depreciation on 3rd year is 25%

Value of the car in 3rd year:-

=> 2,70,000 - (25% of 2,70,000)

=> 2,70,000 - (25/100 × 2,70,000)

=> 2,70,000 - 67,500

=> 2,02,500

Hence, the value of the car in 3rd year is Rs. 2,02,500

Therefore, the value of the car after 3 years will be Rs. 2,02,500