Question

Akshay’s income is \[20\% \] less than that of Ajay. What percent is Ajay’s income more than that of Akshay?

Answer 1

Hint: In the given question, we have to find the percentage of Ajay’s income more than that of Akshay. We are already given the data about Akshay’s income being \[20\% \] less. Here, we can assume the income of Ajay and then rationalize the equation to arrive at the answer.

Complete step by step solution:
Let us understand the concept of percent first.
Calculating percentages is a simple mathematical procedure. If you need to find a ratio or a component of a quantity as a proportion of another quantity, you can express it as a percentage.
To find out the percent of a given number, we can use the following formula:
\[p(\% ) = \dfrac{x}{y} \times 100\]
Where:
\[x\]= Number for which percentage is to be found out;
\[y\]= Total or whole number of given data
We can solve the sum as follows:
First, we need to understand that Akshay’s income is \[20\% \] less than that of Ajay will not mean the same as Ajay’s income being \[20\% \] more than Akshay. For example, \[20\% \] of \[100\] is \[20\] but \[20\% \] of \[20\] is not \[100\].
Let the income of Ajay be Rs. \[100\].
Hence, the income of Akshay will be:
\[100 - 20\% = 100 - (\dfrac{{20}}{{100}} \times 100) = 100 - 20 = 80\] rs.
This also means that Akshay’s income is \[80\% \] of Ajay’s income.
Now if Akshay’s income is Rs. \[1\] then Ajay’s income will be
\[\dfrac{{100}}{{80}} \times 1 = \dfrac{{100}}{{80}}\]rs.
Now if Ajay’s income is \[100\], his income will be more than that of Akshay by following:
\[\dfrac{{100}}{{80}} \times 100 = 125\]
Percentage increase will be-
\[125 - 100 = 25\% \]
Thus, Ajay’s income is \[25\% \] more than that of Akshay.
So, the correct answer is “Option B”.

Note: Alternate method will be as follows:
We know that Akshay’s Income is \[80\% \] of Ajay’s income.
Percentage can be calculated as follows-
\[ = \dfrac{{Ajay's\,Income - Akshay's\,Income}}{{Akshay's\,Income}} \times 100\]
\[ = \dfrac{{100 - 80}}{{80}} \times 100\]
\[ = \dfrac{{20}}{{80}} \times 100\]
\[ = 25\% \]