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Question
The value of a machine depreciates by 15% in the first year and by 12% in the second year. Find the value of the machine if its depreciation in the second year was Rs 1,632.
Solution
Let value of the machine be Rs x.
Vo =Rs x ; n = 2 ; r = 15 %
Depreciation in the first year =
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" "x" xx (1- 15/100)`
`=> "V"_"t" = "Rs" "x" xx 17/20`
`=> "V"_"t" = "Rs" 0.85 "x"`
Depreciation in the second year when r is 12 % =
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" 0.85 "x" xx (1 - 12/100)`
`=> "V"_"t" = "Rs" 0.85 "x" xx 22/25`
`=> "V"_"t" "Rs" 0.748 "x" `
Depreciation in the value of machine in the second year
=Rs (0.85 x-0.748 x) =Rs 1,632
⇒ 0.102 x = Rs 1,632
⇒ x = Rs 16,000
The original value of the machine was Rs 16,000.
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