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 (Solve without using compound interest formula).

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Solution

Let the value of machine in the beginning= Rs. 100
For $1^{st}$ year depreciation $= 10 %$ of Rs. $100 =$ Rs. 100
Value of machine for second year $= 100 - 10$
$=$ Rs. 90
For $2^{nd}$ year depreciation $= 10 %$ of $90 =$ Rs. 9
Value of machine for third year $= 90 - 9$
$=$ Rs. 81
For $3^{rd}$ year depreciation $= 15 %$ of 81
= Rs. $12.15$
Value of machine at the end of third year $= 81 - 12.15$ $=$ Rs. $68.85$
Net depreciation = Rs. 100 - Rs. $68.85$ $=$ Rs. $31.15$
Or $31.15 %$

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