Question

# A motorcycle was bought at $Rs.50000$. The value depreciated at the rate of $8\%$ per annum. Find the value after one year.

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Hint:Depreciating any amount means decreasing its value at some rate in some time. Here the time is one year, so just decrease the principle by $8\%$ of it. This will give you the value of a motorbike after a year with $8\%$ depreciation.

Let’s try to understand what data is given in the question and what do we require. So, in starting the value of motorcycle $\left( P \right)$ is $Rs.50000$ and the rate of depreciation$\left( R \right)$ is given as $8\%$per annum, i.e. the principal money will be depreciated or get reduced at a rate of $8\%$ every year.
That means, if $'n'$ being the time in the year(s), then the amount after the depreciation of principle $\left( P \right)$ at the rate $\left( R \right)$ per annum is $P{\left( {1 - \dfrac{R}{{100}}} \right)^n}$
$\Rightarrow Amount = P{\left( {1 - \dfrac{R}{{100}}} \right)^n}$
Since we have to find the value after one year only, the value of $'n'$ becomes 1
$\Rightarrow Amount = P\left( {1 - \dfrac{R}{{100}}} \right)$
Let’s now substitute the values we know in the equation
$\Rightarrow Amount = 50000 \times \left( {1 - \dfrac{8}{{100}}} \right) = 50000 \times \dfrac{{92}}{{100}}$
Solving the above equation, we can easily find the amount
$\Rightarrow Amount = 500 \times 92 = Rs.46000$
Hence, the value of the motorbike after a year will be $Rs.46000$

Note:Notice that the equation has $\left( {1 - \dfrac{R}{{100}}} \right)$ in it, where subtraction is used before the value is decreasing. The sign will be reversed if the value is increasing at some rate. An alternate approach can be taken by using the concept of the percentage to the principal amount. Since we have to find the value one year, you just need to decrease the principal value by the $8\%$ of the principle. For this, find the $8\%$ of principle first then subtract the same amount from it.