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Question
The value of a machine depreciates by 10%, 12% and 15% in the first 3 years. Express the total depreciation of the machine as a single per cent during the three years.
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Solution
Let value of machine be Rs x.
Vo =Rs x ; n = 3 ; r = 10% for first year, 12 % for 2nd year and 15 % for 3rd year
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" "x" xx (1 - 10/100) (1 - 12/100) (1 - 15/100)`
`=> "V"_"t" = "Rs" "x" xx 9/10 xx 22/25 xx 17/20`
`=> "V"_"t" = "Rs" "x" xx 3366/5000`
⇒ Vt = Rs. 0. 6 732x
Depreciation in the value of car
= Rs (x - 0.6732 x) =Rs 0.3268 x
Percentage change in depreciation
`= (0.3268 "x")/"x" xx 100 `
= 32.68 %
Percentage change = 32.68 %
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