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Question
The value of a 'Honda' bike depreciated by 16% in the first year and by 13% in the second year. Find the value of the bike if it depreciated by Rs 7,098 in the second year.
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Solution
Let value of the bike be Rs x.
Vo =Rs x ; n = 2 ; r = 16 %
Depreciation in the first year =
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" "x" xx (1 - 16/100)^2`
`=> "V"_"t" = "Rs" "x" xx 21/25`
`=> "V"_"t" = "Rs" 0.84 "x"`
Depreciation in the second year when r is 13 % =
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" 0.84 "x" xx (1 - 13/100)`
`=> "V"_"t" = "Rs" 0.84 "x" xx 0.87`
`=> "V"_"t" = "Rs" 0.7308 "x"`
Depreciation in the value of bike in the seoond year
= Rs (0.84 x-0.7308 x) =Rs 7,098
⇒ 0.1092 x = Rs 7,098
⇒ x =Rs 65,000
The original value of the bike was Rs 65,000.
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