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.

Answer 1

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.