Question

A machine was purchased $3$ years ago. Its value decreases by $5\%$ every year. Its present value is $Rs.23000$. For how much money was the machine purchased?

• A. $Rs.16828.45$
• B. $Rs.26826.07$
• C. $Rs.36828.56$
• D. $Rs.46828.80$

Answer 1

The correct option is B $Rs.26826.07$

Given,

Depreciated value $A=Rs.23,000$

Rate of depreciation $R=5\%$

Time $T=3$ years

So, $n=3$

let the machine was purchased in $Rs.P$

Depreciated value,$A=P{(1-\frac{R}{100})}^n$

$\Rightarrow 23000=P\times {(1-\frac{5}{100})}^3$

$\Rightarrow 23000=P\times {(1-\frac{1}{20})}^3$

$\Rightarrow 23000=P\times {\left(\frac{19}{20}\right)}^3$

$\Rightarrow 23000=P\times \frac{19}{20}\times \frac{19}{20}\times \frac{19}{20}$

$\Rightarrow P=23,000\times \frac{20}{19}\times \frac{20}{19}\times \frac{20}{19}$

$\Rightarrow P=26,826.07$

Therefore, the machine was purchased for $Rs.26,826.07$.