# 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. - Mathematics and Statistics

Sum

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.

#### 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.

Concept: Depreciation
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 9 Commercial Mathematics
Miscellaneous Exercise 9 | Q 11 | Page 144