Question

Price of an item is increased by $10\%$ and then decreased by $10\%$ what is net change?

Answer 1

Hint: For this problem we need to calculate the net change in the price of an item according to the given conditions. For this we will first assume the price of the item as $Rs.100$. Given that the price of the item has increased by $10\%$, So we will calculate how much the price has increased and calculate the price after increasing. Now the price of the item has decreased by $10\%$, so we will again calculate how much the price has decreased from the increased price and calculate the price of the item after decreasing it. For net change in the price, we will calculate the difference between the original price and the final price after decreasing.

Complete step-by-step solution:
Let the price of the item will be $Rs.100$.
If the price of the item is increased by $10\%$, then the increment in price will be
$\begin{align}
  & 10\%\text{ of }100=\dfrac{10}{100}\times 100 \\
 & \Rightarrow 10\%\text{ of }100=10 \\
\end{align}$
Now the price of the item after increasing it by $10\%$ will be
$\begin{align}
  & \Rightarrow p=100+10 \\
 & \Rightarrow p=110 \\
\end{align}$
Now the price of the item is decreased by $10\%$, then the decrement in price will be
$\begin{align}
  & \Rightarrow 10\%\text{ of }110=\dfrac{10}{100}\times 110 \\
 & \Rightarrow 10\%\text{ of }110=11 \\
\end{align}$
Now the price of the item after decreasing it by $10\%$ will be
$\begin{align}
  & \Rightarrow p=110-11 \\
 & \Rightarrow p=99 \\
\end{align}$
Now the net change in the price of the item is given by
$\begin{align}
  & \Rightarrow n=100-99 \\
 & \Rightarrow n=1 \\
\end{align}$
Now the one-rupee net change in $Rs.100$ indicates $\dfrac{1}{100}\times 100=1\%$.

Note: For this problem we have assumed the price of the item as $Rs.100$ for a better calculation in solving percentage values. We can also assume the price of the item as $x$ and solve the problem but it is somewhat more difficult than the above procedure.