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Standard IX

Mathematics

Approach to Solve Depreciation Rate Based Questions

Depreciation ...

Question

Depreciation applicable to an equipment is 20%. By how much per cent, will the value of the equipment 3 years from now be less than the present value ?

60%

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54%

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50.8%

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48.8%

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Solution

The correct option is D 48.8%
Let the present value of the equipment be $x$ .
Then, value of the equipment three years from now $= x {(1 - \frac{20}{100})}^{3} = x \times {(\frac{4}{5})}^{3} = \frac{64 x}{125}$
$∴$ Required percentage $= \frac{(x - \frac{64 x}{125})}{x} \times 100 = \frac{(\frac{125 x - 64 x}{125})}{x} \times 100$
$= \frac{61}{125} \times 100 = 48.8 %$

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Depreciation applicable to an equipment is 20%. By how much per cent, will the value of the equipment 3 years from now be less than the present value ?

The correct option is D 48.8%Let the present value of the equipment be x.Then, value of the equipment three years from now =x(1−20100)3=x×(45)3=64x125∴ Required percentage =(x−64x125)x×100=(125x−64x125)x×100=61125×100=48.8%