Question

The value of a machine depreciates at the rate of $10\%$ per annum. It was purchased $3$ years ago. Its present value is $Rs.43740,$ find its purchased price.

Answer 1

Let the purchase price of machine be $Rs.P$
Rate of depreciation $=10\%$ p.a.
Period years.
$\therefore$ Present value $=Rs.43740$
Depreciated value can be calculated by(t)=3

[$\because$ Depriciated value $=A$]

$\Rightarrow Rs.43740=P(1-\frac{10}{100}{)}^3$

$\Rightarrow Rs.43740=P(\frac{9}{10}{)}^3$
$\Rightarrow P=Rs.43740(\frac{10}{9}{)}^3$A=P(1−R100)t

$\Rightarrow P=Rs.43740\times \frac{10}{9}\times \frac{10}{9}\times \frac{10}{9}=Rs.60000$

$\therefore$ Value of machine $3$ years ago $=Rs.60000.$