Question

The value of a machine depreciates from Rs.32768 to Rs.21,952/- in three years. What is the rate of depreciation?

Answer 1

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.