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.

#### Solution

Let value of the soooter be Rs x.

V_{o} =Rs x ; n = 2 ; r = 12 %

Depreciation in the first year =

`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`

`=> "V"_"t" = "Rs" "x" xx (1 - 12/100)`

`=> "V"_"t" ="Rs" "x" xx 22/25 `

`=> "V"_"t" = "Rs" 0.88 "x"`

Depreciation in the second year =

`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`

`=> "V"_"t" = "Rs" 0.88 "x" xx (1 - 12/100)`

`=> "V"_"t" ="Rs" 0.88 "x" xx 22/25 `

`=> "V"_"t" = "Rs" 0.7744 "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.