Question

Thevalue of a machine depreciates at the rate of 10%p.a. After how many full years will the value of tje machine become less than two-thirds of its initial value?
solve it.​

Answer 1

Answer:

$\huge {\mathcal {\red {Given:}}}$

The value of a machine depreciates at the rate of 10%p.a.

$\huge {\mathcal {\green {Solution:}}}$

After one year the value of the machine would be 10% of the initial value i.e.,

= $\large {\frac{1}{10}}$

This means that that the value of the machine becomes $\large {\frac{1}{10}}$ in one year.

Let the number of years in which the initial value of the

machine will become $\large {\frac{2}{3}}$ be x.

Therefore, in one year the value becomes $\large {\frac{1}{10}}$ of the initial value, and in x years the value becomes $\large {\frac{2}{3}}$.

Now,

Time || Value

1 yr ↑ $\large {\frac{1}{10}}$ ↓

x yrs ↑ $\large {\frac{2}{3}}$ ↓

$\large {\frac{1}{x}}$ = $\large {\frac{20}{3}}$

= x = $\large {\frac{3}{20}}$yrs

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