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Question
The value of a car depreciated by 10% in the first 2 years and by 8% in the third year. Express the total depreciation of the car as a single per cent during the three years.
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Solution
Let value of car be Rs x.
`"V"_0` =Rs x ; n = 3 ; r = 10% for first 2 years and 8% for 3rd year .
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" "x" xx (1 - 10/100)^2 (1 - 8/100)`
`=> "V"_"t" = "Rs" "x" xx 9/10 xx 9/10 xx 23/25`
`=> "V"_"t" = "Rs" "x" xx 1863/2500`
`=> "V"_"t" = "Rs" 0.7452 "x"`
Depreciation in the value of car
= Rs (x - 0.7452 x) = Rs 0.2548 x
Percentage change in depreciation
`= (0.2548 "x")/"x" xx 100`
= 25.48 %
Percentage change = 25.48 %
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