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

The value of a property increases every year at the rate of 5%. If its value at the end of 3 years of be Rs 411540, what was its original value at the beginning of these years?
A. 35550.72	B. 35050.72	C. 35050.72	D. 35505.72
Right Option : A
View Explanation

Question : 2

The present price of a scooter is Rs 7290. If its value decreases every year by 10%, then find its value before 3 years.
A. 1000	B. 10000	C. 100000	D. none of these
Right Option : B
View Explanation

Question : 3

The present price of a scooter is Rs 8000. If its value decreases every year by 10%, then find its value before 3 years.
A. 8,88,887.88	B. 8,88,888.88	C. 8,88,886.88	D. none of these
Right Option : B
View Explanation

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