. A piece of equipment cost a certain factory Rs 600000
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?
A: Rs 2,00,000
B: Rs 1,05,000
C: Rs 4,05,000
D: Rs 6,50,000
Let the cost of an equipment is Rs.100.
Now the percentages of depreciation at the end of 1st,2nd,3rd years are 15,13,12 which are in A.P. with a=15 and d=-1.5.
Hence, percentage of depreciation in the tenth year.
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 is 100-82.5=17.5.
The total cost being Rs.600000/100×17.5=Rs 1,05,000
Hence, the total cost is Rs 1,05,000.