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Question
The value of a refrigerator depreciates by 8% of its value at the beginning of the year. Find the original value of the refrigerator if it depreciated by Rs 2,392 in the second year.
Solution
Let value of the refrigerator be Rs x.
Vo =Rs x ; n = 2 ; r = 8 %
Depreciation in the first year =
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" "x" xx (1 - 8/100)`
`=> "V"_"t" = "Rs" "x" xx 23/25`
`=> "V"_"t" = "Rs" 0.92 "x"`
Depreciation in the second year =
`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`
`=> "V"_"t" = "Rs" 0.92 "x" xx (1- 8/100)`
`=> "V"_"t" = "Rs" 0.92 "x" xx 23/25`
`=> "V"_"t" = "Rs" 0.8464 "x" `
Depreciation in the value of refrigerator in the second year
= Rs (0.92 x-0.8464 x) =Rs 2,392
⇒ 0.0736 x = Rs 2,392
⇒ x = Rs 32,500
The original value of the refrigerator was Rs 32,500.
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