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.
Vo =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.
