Question

The price of an article is cut by 10%. To restore it to the original value, the new price must be increased by
1) 10%
2) $9\dfrac{1}{{11}}\% $
3) 11%
4) $11\dfrac{1}{9}\% $

Answer 1

Hint: First let the original price of the article be $x$ and the new price $y$. Formulate the equation according to the given condition. Then, we need to calculate the difference between the original price and the new price. Hence, use the formula \[\dfrac{{{\text{difference}}}}{{{\text{original value}}}} \times 100\] to find the percentage increased.

Complete step-by-step answer:
Let the original price of the article be $x$.
According to the question, the price of the article is cut down by 10%.
Let the new price be $y$.
Since the price $y$ is 10% less than $x$, therefore \[x - \dfrac{{10}}{{100}}x = y\].
$
  0.9x = y \\
  x = \dfrac{y}{{0.9}} \\
$
To increase the price of the article from $y$ to the initial price that is $x$, we first have to calculate the difference of these two prices.
The difference between the old and the new price is the difference by which the new price must be increased to restore it to the original price.
Difference = \[x - y\]
Also we know \[x = \dfrac{y}{{0.9}}\]
Substituting the value of \[x\] to find the difference in terms of the new price, we get
Difference \[ = \dfrac{y}{{0.9}} - y\]
=\[\dfrac{y}{9}\]
The percentage change in the value can be calculated by the formula \[\dfrac{{{\text{difference}}}}{{{\text{original value}}}} \times 100\]
Here the original value is the new price that is $y$, and the difference is \[\dfrac{y}{9}\].

Substituting the value of difference and the original value to calculate the percentage change, we get
Percentage Change \[ = \dfrac{y}{{9y}} \times 100\]
=$11\dfrac{1}{9}\% $
Hence, option D is the correct answer.

Note: This question can alternatively be done by letting the original price and Rs 100. Then find the new price after the price of an article is cut by 10%. Then, find the new percentage increased by using the formula, \[\dfrac{{{\text{difference}}}}{{{\text{original value}}}} \times 100\].Also, the original value is the value that comes after the price is cut by 10%.