Question

Anant purchased an old motorbike for Rs16000. If the value of the motorbike after 2 years is Rs14440 ,find the rate of depreciation.​

Answer 1

Answer:

$\red{\underbrace{\underline{\bigstar\:\bf Required\:Answer:}}}$

$\sf {Cost \: price \: of \: the \: motorbike(c) \: = \: Rs \: 16000}$

$\sf \: Let \: the \: Rate \: of \: depreciation \: = \: d %</p><p></p><p>$

$\sf \orange{Motorbike \: price \: after \: 2 \: years}$

$\pink{S = Rs \: 14440}$

$\sf \: S = c ×(100 - d )/100× (100-d)/100$

$\sf14440 = 16000 × (100 - d )^2 /10000$

$\sf \gray{ \:( 14440 × 10000)/16000 = ( 100 - d )^2}$

$\sf \green{( 144400/16) = ( 100 - d )^2}$

$\sf \blue{9025 = ( 100 - d )^2}$

$\sf\purple{95 = 100 - d}$

$\sf\red{d = 100 - 95}$

$\sf \:d = 5 %$

$\sf \: Rate \: of \: the \: depreciation \: = d = 5\%$

Answer 2

Answer:

Answer

It is given that

CP of an old motorbike = 16000

Price after 2 years = 14440

Consider r% as the rate of depreciation

We know that

A/P = (1−r/100)

n

Substituting the values

14440/16000=(1−r/100)

2

By further calculation

361/400=(1−r/100)

2

(19/20)

2

=(1−r/100)

2

So we get

19/20=1−r/100

r/100=1−19/20=(20−19)/20=1/20

By cross multiplication

r=100/20=5

Hence, the rate of depreciation is 5%