Question

The price of an article is increased by $25\%$ by how much percent must this new value be decreased to restore it to its former value

Answer 1

Finding the decrease percent:

Lets the price of the article $=₹100$

The price of the article is increased by $25\%$

Increase in price of the article is

$$\begin{gathered} =25\%\mathrm{of}₹100 \\ =\frac{25}{100}\times 100 \\ =₹25 \end{gathered}$$

Therefore, the new increased price $=₹100+₹25=₹125$

So, if we subtract $₹25$ from $₹125$, we get the original price of article.

Therefore, decrease in percent is

$$\begin{gathered} =\frac{\mathrm{Decrease}\mathrm{in}\mathrm{price}}{\mathrm{New}\mathrm{increased}\mathrm{price}}\times 100 \\ =\frac{25}{125}\times 100 \\ =\frac{1}{5}\times 100 \\ =20\% \end{gathered}$$

Hence, the new value must be decreased by $20\%$ to get its former value.