Page 134 - ICSE Math 8

Let the value of the house after 2 years be A.

Ê R ˆ n Ê 20 ˆ 2
A = P 1- 100¯ = 50,00,000 1- 100¯ ˜
Á
Á
˜
Ë
Ë
Ê 1ˆ 2 Ê 4ˆ 2
= 50,00,000 1- 5¯ = 50,00,000 Á ˜
Á
˜
Ë
5¯
Ë
4 4
= 50,00,000 × × = ` 32,00,000
5 5
The builder gets ` 32,00,000 for the house after 2 years.
Example 21: A new computer costs ` 80,000. Due to advancement in technology, its value depreciates every
year. If the rates of depreciation are 4%, 5% and 10% in the three successive years, find its
value after 3 years.
Solution: Original value of the computer (P) = ` 80,000

Rate of depreciation in the first year = 4%
Rate of depreciation in the second year = 5%
Rate of depreciation in the third year = 10%
Let the depreciated value be A.

Ê 4 ˆ Ê 5 ˆ Ê 10 ˆ Ê 1 ˆ Ê 1 ˆ Ê 1 ˆ
\ A = 80,000 1- 100¯ Ë 1- 100¯ Ë 1- 100¯ ˜ = 80,000 1- 25¯ Ë 1- 20¯ Ë 1- 10¯
˜
Á
˜ Á
˜ Á
Á
˜ Á
˜ Á
Ë
Ë
Ê 24ˆ Ê 19ˆ Ê 9 ˆ
= 80,000 Á Ë 25¯ Ë 20¯ Ë 10¯ ˜ = 65,664
˜ Á
˜ Á
Hence, the depreciated value of the computer after 3 years is ` 65,664.
EXERCISE 11.6
1. The cost of a generator is ` 1,60,000. If its value depreciates at the rate of 5% per annum, what will be
its value after: (a) 2 years (b) 3 years

2. Sonika bought a car for ` 5,50,000. The value of the car depreciates at the rate of 5% every six months.
What is the value of the car after 2 years?
3. The price of silver at present is ` 8,000 per kg. Its price increases at the rate of 5% in the first year,
decreases at the rate of 10% in the second year and again decreases further at the rate of 4% in the third
year. Find its price per kg at the end of the third year.

4. A car costs ` 2,40,000. Its value depreciates at the rate of 5% every year. If after some time period, its
value is ` 2,05,770, find the time period.

5. The cost of a new washing machine is ` 22,000. Its value depreciates every year. If the depreciated value
of the washing machine after 2 years is ` 14,080, find the rate of depreciation.
6. The present price of a sofa set is ` 7,290. If its value decreases every year by 10%, then find its value
before 3 years.
7. The value of a flat worth ` 5,00,000 is depreciating at the rate of 10% per annum. In how many years
will its value be reduced to ` 3,64,500?

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