Question

# The cost of the machine is 2,50,000/-. If the rate of depreciation is 10% per year. Find the depreciation in the price of the machine after 2 years.

Hint: Find the price after 1 year by calculating. Then find the price after two years. Subtract the price after two years from the cost price to get depreciation in the price of the machine after 2 years.

Let C be the cost price of the machine.

Let d be the rate of depreciation.

Given Data
C = 2,50,000 and d = 10%

Let P1 and P2 be the price of the machine after 1 year and 2 years respectively.

P1 = Cost price – rate loss due to depreciation in first year
Rate loss due to depreciation in 1 year can be determined as = $\dfrac{{{\text{C}} \times {\text{d}}}}{{100}}$
= $\dfrac{{2,50,000{\text{ }} \times {\text{ 10}}}}{{100}}$
= 25,000/-

Hence, P1 = C – $\dfrac{{{\text{C}} \times {\text{d}}}}{{100}}$
= 2,50,000 – 25,000
P1 = 2,25,000/-

Now, P2 = Price after one year – Rate loss due to depreciation in second year
Rate loss due to depreciation in second year =$\dfrac{{{\text{C}} \times {\text{d}}}}{{100}}$, for P2 Cost price C is nothing but P1, hence =$\dfrac{{{\text{P1}} \times {\text{d}}}}{{100}}$
= $\dfrac{{2,25,000{\text{ }} \times {\text{ 10}}}}{{100}}$
= 22,500/-

Hence, P2 = P1 – (P1 x d)/100
= 2,25,000 – 22,500
P2 = 2,02,500/-

The depreciation after two years can be computed as = Cost price – Price after two years
= C – P2
= 2,50,000 – 2,02,500
= 47,500/-

Note: In order to solve these types of questions, the key is to use the percentage formula correctly to find out the rate lost due to depreciation. Another thing to keep in mind is that while calculating the price after two years the original cost price should not be used but instead the price after one year should be used because there’s been a change already in that whole year.