Problems on Depreciation


 
 
Concept Explanation
 

Problems on Depreciation

It is well known fact that the constant use of any machine or any other article causes wear and tear due to which its value decreases with time.

Depreciation:  The relative decrease in the value of a machine over a period of time is called its depreciation.

Rate of Depreciation: Depreciation per unit time is called the rate of depreciation.

Depreciated Value: The value at any time is called the depreciated value.

Formulae for Depreciation:

Formula1:  If V_{0} be the value of an article at a certain time and R% per annum is the rate of depreciation, then the value V_{n} at the end of n years is given by

V_{n}=V_{0}left ( 1-frac{R}{100} right )^{n}

Formula 2: If  V_{0} is the value of an article at certain time and the rate of depreciation is R_{1}% for first n_{1} years, r_{2}% for next n_{2} years and so on and R_{k}% for the last n_{k} years, then the value at the end of n_{1}+n_{2}+...+n_{k} is given by

V=V_{0}left ( 1-frac{R_{1}}{100} right )^{n_{1}}left ( 1-frac{R_{2}}{100} right )^{n_{2}}...left ( 1-frac{R_{k}}{100} right )^{n_{k}}

Illustration: Jack purchased an old scooter for Rs 16000. If the cost of scooter after 2 years depreciates to Rs 14440, find the rate of depreciation

Solution: Let the rate of depreciation be R% per year. Then,

14440=16000left ( 1-frac{R}{100} right )^{2}

frac{1444}{1600}=left ( 1-frac{R}{100} right )^{2}

frac{361}{400}=left ( 1-frac{R}{100} right )^{2}

left (frac{19}{20} right )^{2}=left ( 1-frac{R}{100} right )^{2}

Take square root on both sides, we have

frac{19}{20} = 1-frac{R}{100}

frac{R}{100} =1-frac{19}{20}

frac{R}{100} =frac{1}{20}

R =frac{100}{20}

R =5

Hence, the rate of depreciation is 5% pr annum.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A new car costs Rs 360000. Its price depreciates at the rate of 10% a year during the first two years and at the rate of 20 % a year thereafter . What will be the price of the car after 3 years?

Right Option : C
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Question : 2

The cost of a T.V set was quoted Rs 17000 at the beginning of 1999. In the beginning of 2000 the price was hiked by 5%. Because of decrease in demand the cost was reduced by 4% in the beginning of 2001. What is the cost of the T.V. set in 2001?

Right Option : A
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Question : 3

The value of a flat worth Rs 500000 is depreciating at the rate of 10% per annum. In how many years will its value be reduced to Rs 364500?

Right Option : A
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