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Question
A building worth Rs. 121000 is constructed on land worth Rs. 81000. After how many years will the value of both be the same if land appreciates at 10% pa. and buildings depreciate at 10% p.a.
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Solution
Given,
Value of the building = V.B. = ₹ 1,21,000
Value of land = V.L. = ₹ 81,000/-
Rate of appreciation of land = rate of depreciation of building = r = 10%.
For the value of building and land to be the same.
V.L.`(1 + "r"/100)^"n" = "V"."B".(1 - "r"/100)^"n"`
∴ `81,000(1 + 10/100)^"n" = 1,21,000(1 - 10/100)^"n"`
`81,000(11/10)^"n" = 1,21,000(9/10)^"n"`
∴ `(11^"n")/(10^"n") xx (10^"n")/(9^"n") = (1,21,000)/(81,000)`
∴ `(11^"n")/(9^"n") = (11^2)/(9^2)`
∴ n = 2 years.
∴ After two years the value of the building and land will be the same.
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