Question:
If the numerator of a fraction is increased by 15% and its denominator is decreased by 10%, then the percentage of increase in that fraction is
If the numerator of a fraction is increased by 15% and its denominator is decreased by 10%, then the percentage of increase in that fraction is
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For percentage increase/decrease problems involving fractions, multiply the individual change factors first and then compare with 1.
Updated On: Jun 15, 2026
- \( 28\frac{5}{9} \)
- \( 27\frac{7}{9} \)
- \( 27\frac{2}{9} \)
- \( 26\frac{4}{9} \)
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The Correct Option is B
Solution and Explanation
Step 1: Assume the original fraction.
Let the original fraction be \[ \frac{N}{D} \] After the changes, \[ \text{New Fraction} = \frac{1.15N}{0.90D} \] \[ = \frac{115}{90}\cdot\frac{N}{D} = \frac{23}{18}\cdot\frac{N}{D} \]
Step 2: Determine the increase factor.
The fraction becomes \[ \frac{23}{18} \] times its original value. Hence increase factor is \[ \frac{23}{18}-1 = \frac{5}{18} \]
Step 3: Convert into percentage.
\[ \frac{5}{18}\times100 = \frac{500}{18} = \frac{250}{9} = 27\frac79\% \] Therefore, \[ \boxed{27\frac79\%} \]
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