a machine depreciates in value at the rate of 30%   every year in the reducing balance. if the original cost be rs 20000 and ultimate scrap value be rs 4802. find the effective life of the machine.

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Scrap} \mathrm{value}=\mathrm{Original} \mathrm{Cost}{\left(1-\frac{\mathrm{Rate} \mathrm{of} \mathrm{Depreciation}}{100}\right)}^{\mathrm{Effective} \mathrm{life}} \\ \mathrm{Let} \mathrm{effective} \mathrm{life} \mathrm{be} \mathrm{n} \\ 4802=20000{\left(1-\frac{30}{100}\right)}^{\mathrm{n}} \\ \Rightarrow \frac{4802}{20000}={\left(\frac{7}{10}\right)}^{\mathrm{n}} \\ \Rightarrow \frac{2401}{10000}={\left(\frac{7}{10}\right)}^{\mathrm{n}} \\ \Rightarrow {\left(\frac{7}{10}\right)}^4={\left(\frac{7}{10}\right)}^{\mathrm{n}} \\ \mathrm{n}=4 \mathrm{years} \left[\mathrm{Answer}\right] \end{gathered}$$

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