A manufacturer reckons that value of a machine, which costs him Rs. 15625 will depreciate each year

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8. Sequences and Series

hard

A manufacturer reckons that the value of a machine, which costs him $Rs.$ $15625$ will depreciate each year by $20 \% .$ Find the estimated value at the end of $5$ years.

$Rs$ $5120$

Solution

cost of machine $= Rs .15625$

Machine depreciates by $20 \%$ every year.

Therefore, its value after every year is $80 \%$ of the original cost i.e., $\frac{4}{5}$ of the original cost.

$\therefore $ Value at the end of $5$ years $ = 15625 \times \underbrace {\frac{4}{5} \times \frac{4}{5} \times \ldots \times \frac{4}{5}}_{5\,\,\,times} = 5 \times 1024 = 5120$

Thus, the value of the machine at the end of $5$ years is $Rs.$ $5120 .$

Standard 11

Mathematics

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medium

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hard

(JEE MAIN-2013)

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medium

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easy

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hard

(JEE MAIN-2019)

A manufacturer reckons that the value of a machine, which costs him $Rs.$ $15625$ will depreciate each year by $20 \% .$ Find the estimated value at the end of $5$ years.

Solution

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