Question

A’s income is 20% less than that of B’s. How much percent is B’s income is more than A’s?

Answer 1

Hint: In this problem, first we need to find the income of A and B in one variable. Next, find the percent increase in income of B. In percentage increase formula, we need to divide by A’s income instead of B’s income because, here we need to find increase in B’s income with respect to A’s income.

Complete step by step answer:
Let the income of B be Rs.\[x\].
Since, A’s income is 20% less than that of B’s, the income of A is calculated as follows:
\[
  \,\,\,\,\,\,{\text{A's}}\,\,{\text{income}} = \left( {100 - 20} \right)\% {\text{of}}\,\,{\text{B}} \\
   \Rightarrow {\text{A's}}\,\,{\text{income}} = \dfrac{{80}}{{100}} \times x \\
   \Rightarrow {\text{A's}}\,\,{\text{income}} = 0.80x \\
\]
Now, the percent increase in amount of B is calculated as follows:
\[
  \,\,\,\,\,{\text{Percent increase in amount of B = }}\dfrac{{{\text{amount of B - amount of A}}}}{{{\text{amount of A}}}} \times 100 \\
   \Rightarrow {\text{Percent increase in amount of B = }}\dfrac{{x - 0.8x}}{{0.80x}} \times 100 \\
   \Rightarrow {\text{Percent increase in amount of B = }}\dfrac{{0.2x}}{{0.80x}} \times 100 \\
   \Rightarrow {\text{Percent increase in amount of B = }}0.25 \times 100 \\
   \Rightarrow {\text{Percent increase in amount of B = }}25 \\
\]

Thus, B’s income is 25% more than A’s income.

Note: The percent increase in amount of B is obtained by dividing the income of A instead of B in percentage increase formula. To find the percent increase, first subtract the initial value from the final value and then take the difference and divide it by initial value. Next, multiply the result by 100 to convert the number into percentage.