Question

A number is increased by 20% and then again by 20%. By what percent should an increased number be reduced so as to get back the original number?
A. \[30\dfrac{5}{9}\% \]
B. \[40\dfrac{5}{9}\% \]
C. \[40\% \]
D. \[30\% \]

Answer 1

Hint:To solve this problem, understanding of percentage is necessary.
Percentage formula is used to find the amount or share of something in terms of 100. In its simplest form, percent means per hundred. To express a number between zero and one, a percentage formula is used. It is defined as a number represented as a fraction of 100. Denoted by the symbol %, the percentage is majorly used to compare and find out ratios.


Complete step by step solution:
Percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in percentage.
Let’s take the number = x
1 percent of \[x = \dfrac{x}{{100}} \times 1\]
Then
20% of \[x = \dfrac{x}{{100}} \times 20\]
Adding x % to the quantity itself of in the other words \[\left( {100 + x} \right)\% \]of that quantity
Similarly decreasing a quantity by x% means \[\left( {100 - x} \right)\% \]of the quantity.
According to the question
Let the number be \[100\% \]
Increasing 100 by 20% means
\[ \Rightarrow \left( {100 + 20} \right) \times \dfrac{{100}}{{100}}\]
\[ \Rightarrow 120\]
Now increasing 120 by 20%
\[ \Rightarrow \dfrac{{120}}{{100}} \times \left( {100 + 20} \right)\]
\[ \Rightarrow \dfrac{{120}}{{100}} \times 120\]
\[ = 144\]
Now we need to find the percentage of 144 which can take us back to 100, the original number i.e. 44.
Therefore
x% of 144 is 44
\[ \Rightarrow \dfrac{x}{{100}} \times 144 = 44\]
\[ \Rightarrow x = \dfrac{{44 \times 100}}{{144}}\]
\[ \Rightarrow x = 30\dfrac{5}{9}\% \]
Hence option (a) is correct.


Note:Generally, in this type of questions, an increment of 20 % is taken two times so you should not just sum it up and take it as 40 % because after the first increment the base value will be changed for the second increment of 20 %. So, students should not be confused about that.