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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.
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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.
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