Question

The price of an article has increased by 25%. By how much percent must this new value be decreased to restore it to its former value?

Answer 1

Hint: Assume that the initial price of the article is Rs. \[x\] . The new price of the article is Rs. \[x\] + 25% of \[x\] . The amount that must be deducted from the new price to restore its price to its former value must be equal to the difference between the new price of the article and the initial price of the article. Now, solve it further and calculate the percentage that must be decreased from the new price of the article to restore it to its former value

Complete step-by-step answer:
According to the question, we are given that the price of an article is increased by 25% and we are asked to find out the percent decrease in the new value to restore it to its former value.
First of all, let us assume that the initial price of the article is Rs. \[x\] ………………………………..(1)
After an increment of 25%, the new price of the article must be equal to
= \[x\] + 25% of \[x\]
\[\begin{align}
  & =x+\dfrac{25}{100}\times x \\
 & =x+\dfrac{x}{4} \\
\end{align}\]
\[=\dfrac{5x}{4}\] ………………………………………………..(2)
From equation (2), we have
The new price of the article = Rs. \[\dfrac{5x}{4}\] …………………………………………..(3)
From equation (1), we have the initial price of the article.
To restore the price to the original price, the price of the article must be equal to Rs. \[x\] .
The amount that must be deducted from the new price must be equal to the difference between the new price of the article and the initial price of the article ……………………………………(4)
Now, from equation (1), equation (3), and equation (4), we get
The amount to be decreased from the new price of the article \[=\dfrac{5x}{4}-x=\dfrac{x}{4}\] ………………………………(5)
For percentage of decreased amount, we have
\[=\dfrac{\dfrac{x}{4}}{\dfrac{5x}{4}}\times 100=\dfrac{1}{5}\times 100=20\]
Therefore, the percent by which the new price must be decreased to restore it to the original price is 20%.

Note: We can also solve this question, by assuming the original price of the article is equal to Rs. 100.
Since the price has been increased by 25% so, the new price of the article is,
= (100 + 25% of x)
\[\begin{align}
  & =100+\dfrac{25}{100}\times 100 \\
 & =100+25 \\
 & =125 \\
\end{align}\]
The new price of the article = Rs. 125.
To restore the price to the original price, the price of the article must be equal to Rs. 100.
The amount to be decreased from the new price of the article = Rs. \[125-100\] = Rs. 25
For percentage of decreased amount, we have
\[=\dfrac{25}{125}\times 100=\dfrac{1}{5}\times 100=20\]
Therefore, the percent by which the new price must be decreased to restore it to the original price is 20%.