Question

The value of a machine depreciates every year by 10%. If the present value of the machine is Rs 54000, what was its value last year?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{machine}\mathrm{last}\mathrm{year}\mathrm{be}\mathrm{Rs}\mathrm{x}. \\ \mathrm{Then},\mathrm{its}\mathrm{present}\mathrm{value}=90\%\mathrm{of}\mathrm{Rs}\mathrm{x} \end{gathered}$$
$$\begin{gathered} =Rs\left(x\times \frac{90}{100}\right) \\ =Rs\frac{90x}{100} \end{gathered}$$
$$\begin{gathered} \mathrm{Now},\frac{90\mathrm{x}}{100}=54000 \\ \Rightarrow \mathrm{x}=\left(54000\times \frac{100}{90}\right) \\ \Rightarrow \mathrm{x}=\mathrm{Rs}60000 \end{gathered}$$
$\mathrm{Hence},\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{machine}\mathrm{last}\mathrm{year}\mathrm{was}\mathrm{Rs}60,000.$