Question

The value of a scooter depreciates by 12% of its value at the beginning of the year. Find the original value of the scooter if it depreciated by Rs 2,640 in the second year.

Answer 1

Let value of the soooter be Rs x. 

V_o =Rs x ; n = 2 ; r = 12 % 

Depreciation in the first year = 

${\displaystyle \therefore {\text{V}}_{\text{t}}={\text{V}}_0\times {(1-\frac{\text{r}}{100})}^{\text{n}}}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} \text{x}\times (1-\frac{12}{100})}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} \text{x}\times \frac{22}{25}}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} 0.88 \text{x}}$

Depreciation in the second year = 

${\displaystyle \therefore {\text{V}}_{\text{t}}={\text{V}}_0\times {(1-\frac{\text{r}}{100})}^{\text{n}}}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} 0.88 \text{x}\times (1-\frac{12}{100})}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} 0.88 \text{x}\times \frac{22}{25}}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} 0.7744 \text{x}}$

Depreciation in the value of soooter in the second year 

=Rs (0.88 x - 0.7744 x) =Rs 2,640 
⇒  0.1056 x = Rs 2,640 
⇒  x =Rs 25,000 
The original value of the soooter was Rs 25,000.