Question

the cost of a article depreciates by Rs.11250during second year and by Rs.9112.50 during fourth year calculate rate of depreciation per annum and original cost of article

Answer 1

method of depreciation will be "reducing balance method" as it is evident that the depreciation amount decreases as the time progresses..

let P be the value of the article

n be the no.of years

i be the rate of depreciation per annum

The cost of a article depreciates by Rs.11250during second year

P(1- i)^2= 11250.......(1)

by Rs.9112.50 during fourth year

P(1- i)^4= 9112.50.......(2)

now (2) / (1)

P(1- i)^4/P(1- i)^2 = 9112.50/ 11250

(1- i)^2  = 0.81

(1- i)^2 = 81/100

(1- i) = root over 81/100

(1- i) = 9/10 =0.9

1-0.9 = i

0.1 = i

i = 0.1 or 10/100 = 10%... so the depreciation rate = 10%

substituting i in (1) ...

P(1- i)^2= 11250

P(1- 10%)^2= 11250

P(1- 0.1)^2= 11250

P(0.9)^2= 11250

p(0.81) = 11250

p = 11250/0.81 = 13889..

so the the original cost of the article is 13889 ..and the rate of depreciation = 10%