Question:
The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, then it becomes 3/4. The fraction is
The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, then it becomes 3/4. The fraction is
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Always convert word problems on fractions into equations and solve step-by-step.
Updated On: Aug 11, 2025
- 25/26
- 35/26
- 26/35
- 25/36
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The Correct Option is D
Solution and Explanation
Let the numerator be \(x\), then the denominator is \(x + 11\).
After adding 8 to both, the fraction becomes: \[ \frac{x + 8}{x + 19} = \frac{3}{4} \] Cross multiplying: \[ 4(x + 8) = 3(x + 19) \] \[ 4x + 32 = 3x + 57 \] \[ x = 25 \] So, the fraction is \(\frac{25}{25 + 11} = \frac{25}{36}\).
After adding 8 to both, the fraction becomes: \[ \frac{x + 8}{x + 19} = \frac{3}{4} \] Cross multiplying: \[ 4(x + 8) = 3(x + 19) \] \[ 4x + 32 = 3x + 57 \] \[ x = 25 \] So, the fraction is \(\frac{25}{25 + 11} = \frac{25}{36}\).
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