Question

A's income is 20% less than that of B; by what percent is B's income more than that of A's?

Answer 1

Hint: Start this question by assuming the income of B as x. Then calculate the income of A in terms of B, according to the above condition given. Now, calculate how much the value of B's income is more than A and then divide by the value of A's income to get the answer.
I hope the hint is sufficient to solve the question; however if you find difficulty solving the question, you can refer to the solution below.

Complete step-by-step answer:
Now, let us take the income of B as x.
\[ \Rightarrow B = x\]
Now, the income of a is 20% less than B. Therefore, let us calculate it
\[ \Rightarrow A = x - 20\% x\]
\[ \Rightarrow A = x - \dfrac{{20}}{{100}}x\]
\[ \Rightarrow A = \dfrac{4}{5}x\]
Now, we have both A's and B's income.
To calculate by how much B's income is more than A's, let us subtract the income of A from B as shown below,
\[ \Rightarrow B - A = x - \dfrac{4}{5}x\]
\[ \Rightarrow B - A = \dfrac{1}{5}x\]
Now, to calculate the difference in percentage, let us divide the difference by A's income to get the fraction shown below,
\[ \Rightarrow \dfrac{{B - A}}{A} = \dfrac{{\dfrac{1}{5}x}}{{\dfrac{4}{5}x}}\]
\[ \Rightarrow \dfrac{{B - A}}{A} = \dfrac{1}{4}\]
Now, multiply the fraction by 100 to get the percentage by which B's income is more than A.
\[ \Rightarrow \dfrac{{B - A}}{A} \times 100\% = \dfrac{1}{4} \times 100\% \]
\[ \Rightarrow \dfrac{{B - A}}{A} \times 100\% = 25\% \]
Thus, the required answer is \[25\% \].
So, the correct answer is “\[25\% \]”.

Note: In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", A percentage is a dimensionless number; it has no unit of measurement. It does not have any units as it is a ratio of quantities with the same unit multiplied by 100.