Question

The value of a machine depreciated by 10 % per year during the first two years and 15 % per year during the third year. Express the total depreciation of the machine ,as percent, during the three years.

• A. 31.15 %
• B. 15.15 %
• C. 30 %
• D. 25.25%

Answer 1

The correct option is A

31.15 %

Let the value (Principal) of the machine (P) = ₹ 100
Rate of depreciation for the first year (R) =10%
∴ Value of machine at the end of first year = ₹ ( 100-$\frac{100\times 10}{100}$) = ₹ 90
Rate of depreciation for the second year =10 %
∴ Value of machine at the end of second year= ₹ (90-$\frac{90\times 10}{100}$) = ₹ 81
Rate of depreciation for the third year =15%
∴ Value of machine at the end of third year = ₹ (81-$\frac{81\times 15}{100}$)
= ₹ $\frac{8100-1215}{100}$
= ₹ 68.85
Total depreciation = ₹ (100.00− 68.85 )= ₹ 31.15
Percentage of depreciation = 31.15 x $\frac{100}{100}$ % = 31.15%