Advertisements
Advertisements
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.
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.
APPEARS IN
RELATED QUESTIONS
Kanchan purchased a Maruti car for Rs.2,45,000/- and the rate of depreciation is `14 2/7 %` per annum. Find the value of the car after two years?
The value of a machine depreciates from Rs.32768 to Rs.21,952/- in three years. What is the rate of depreciation?
The value of a machine depreciates at a rate of 10% every year. It was purchased 3 years ago. Its present value is Rs.2,18,700/-. What was the purchase price of the machine?
Mr. Manish purchased a motorcycle at Rs.70,000/-. After some years he sold his motorcycle at the exact depreciated value of it that is Rs.51,030/-. The rate of depreciation was taken as 10%. Find after how many years he sold his motorcycle.
Mr. Chetan purchased furniture for her home at Rs.5,12,000/-. Considering the rate of depreciation as 12.5%, what will be the value of furniture after 3 years.
Grace Fashion Boutique purchased a sewing machine at Rs.25,000/-. After 3 years machine was sold at a depreciated value Rs.18,225/- Find the rate of depreciation.
Mr. Pritesh reduced the value of his assets by 5% each year, which were purchased for Rs.50,00,000/-. Find the value of assets after 2 years.
A manufacturing company is allowed to charge a 10% depreciation on its stock. The initial value of the stock was Rs.60,000/-. After how many years the value of the stock will be 39366?
The value of the machine depreciates at the rate of 15% p.a. It was purchased 2 years ago. Its present value is Rs. 7225. What was the purchase price of the machine?
A tree increases annually by 1/8 of its height. By how much will it increase after 2½ years. If its length today is 8 m.?
What is ‘Depreciation’?
