Question

Ajay gets 20% less marks than that of Vatsal’s marks. By what percent Vatsal’s mark is more than Ajay’s marks?

Answer 1

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

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

Thus, Vatsal’s marks is 25% more than Ajay’s marks.

Note: The percent increase in Vatsal’s marks is obtained by dividing the Ajay’s marks instead of Vatsal’s marks 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.