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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.
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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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