Question:
Two numbers are \(20\%\) and \(30\%\) less than a third number. What percentage of second number is first number?
Two numbers are \(20\%\) and \(30\%\) less than a third number. What percentage of second number is first number?
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In percentage comparison problems, assume the original number as \(100\) for faster calculation.
Updated On: Jul 15, 2026
- \(124\frac{3}{7}\%\)
- \(111\frac{3}{7}\%\)
- \(124\frac{2}{7}\%\)
- \(114\frac{2}{7}\%\)
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The Correct Option is D
Solution and Explanation
Concept:
Take the third number as the base.
Step 1: Assume the third number.
Let the third number be: \[ 100 \] Then: First number is \(20\%\) less: \[ 100-20=80 \] Second number is \(30\%\) less: \[ 100-30=70 \]
Step 2: Find what percent second number is first number.
Required: \[ \frac{\text{First}}{\text{Second}}\times 100 \] \[ =\frac{80}{70}\times100 \] \[ =\frac87\times100 \] \[ =\frac{800}{7} \] \[ =114\frac27\% \] Thus, the required answer is: \[ \boxed{114\frac27\%} \]
Step 1: Assume the third number.
Let the third number be: \[ 100 \] Then: First number is \(20\%\) less: \[ 100-20=80 \] Second number is \(30\%\) less: \[ 100-30=70 \]
Step 2: Find what percent second number is first number.
Required: \[ \frac{\text{First}}{\text{Second}}\times 100 \] \[ =\frac{80}{70}\times100 \] \[ =\frac87\times100 \] \[ =\frac{800}{7} \] \[ =114\frac27\% \] Thus, the required answer is: \[ \boxed{114\frac27\%} \]
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