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# The cost of a machine is $Rs.\,32000.$ Its value depreciates at the rate of $5\%$ every year. Find the total depreciation in its value by the end of $2$ years.(A) $Rs.\,3210$(B) $Rs.\,3690$(C) $Rs.\,4230$(D) $Rs.\,5150$

Last updated date: 13th Jun 2024
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Hint: In this question the depreciation rate is given so with the help of depreciation we can easily find the depreciated cost of the machine at the end of each year. Now, we will subtract the depreciated cost of the machine from the actual cost of the machine to find the depreciation at the end of $2$ years.

Complete step-by-step solution:
The cost of a machine is given $Rs.\,32000.$ Its depreciation rate is given $5\%$
Now, with the help of depreciation rate we can find depreciated value at the end of first year
The depreciated value at the end of first year is $= 32000 \times \dfrac{5}{{100}} = 1600$
Therefore, depreciated value at the end of first year is $Rs.\,1600$ .
Now, the value of a machine after first year is $Rs.\,32000 - Rs.\,1600 = Rs.\,30400$
Now, we will again find the depreciated value for the second year
The depreciated value at the end of second year is $= 30400 \times \dfrac{5}{{100}} = 1520$
Therefore, depreciated value at the end of first year is $Rs.\,1520$ .
Now, we will add the depreciated value in the cost of a machine at the end of $2$ years to find the total depreciation in its value by the end of $2$ years.
$\Rightarrow Rs.\,1600 + Rs.\,1520 = Rs.\,3120$

Hence, the correct option is (A)

Note: In this question the important thing is that the depreciated value after the second year is calculated on the depreciated value of a machine after the first year. So be careful while calculating the depreciated value if asked for more years. We can also calculate the value by calculating the depreciated value of a machine at the end of each year.