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Question
The value of a machine depreciates from Rs.32768 to Rs.21,952/- in three years. What is the rate of depreciation?
Solution
Given, the initial value of machine = V
= ₹ 32,768/-
The depreciated value of the machine = D.V.
= ₹ 21,952/-
Number of years = n = 3
Using D.V. = V `(1 - "r"/100)^"n"`
`21,952 = 32,768 (1 - "r"/100)^3`
∴ `(1 - "r"/100)^3 = (21,952)/(32,768)`
∴ `1 - "r"/100 = root{3}((21,952)/(32,768))`
= `root{3}((2^6 xx 7^3)/(2^15))`
= `root{3}(((2^2 xx 7)/(2^5))^3)`
∴ `(100 - "r")/100 = 7/8`
800 - 8r = 700
r = `100/8`
∴ r = 12.5%
∴ The rate of depreciation is 12.5% per annum.
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What is ‘Depreciation’?
