Question

In a factory, the cost of a machine is ₹ 6,00,000. If its value depreciates 15% the first year, 13.5 % the next year, 12% the third year, and so on. Calculate its value at the end of 10 years, applying all percentages to the original cost?

• A. ₹ 1,00,000
• B. ₹ 1,05,000
• C. ₹ 1,50,000
• D. ₹ 1,05,650

Answer 1

The correct option is B

₹ 1,05,000

Suppose that the cost of machine be ₹ 100.

Now the percentages of depreciation at the end of first, second, third years are 15, 13.5, 12, which are in A.P

Here, 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 = $\frac{10}{2}(15+1.5)$ = ₹ 82.50

Hence, the value of equipment at the end of 10 years = 100 - 82.5 = ₹ 17.5

The total cost being Rs. 6,00,000/100 * 17.5 = ₹ 1,05,000