A piece of equipment cost a certain factory 6,00,000. If it depreciates in value, 15% the first year, 13.5% the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?

Solution(By Examveda Team)

Let the cost of an equipment is Rs. 100
Now the percentages of depreciation at the end of 1st, 2^nd, 3^rd years are 15, 13.5, 12, which are in A.P., with a = 15 and d = - 1.5
Hence, percentage of depreciation in the tenth year = a + (10 - 1) d = 15 + 9 (-1.5) = 1.5
Also total value depreciated in 10 years = 15 + 13.5 + 12 + ..... + 1.5 = 82.5
Hence, the value of equipment at the end of 10 years = 100 - 82.5 = 17.5
The total cost being
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,\frac{{6,00,000}}{{100}} \times 17.5 \cr & = {\text{Rs}}{\text{.}}\,1,05,000 \cr} $$