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 \( \frac{3}{4} \). The fraction is

Show Hint

Adding the same number to top and bottom keeps their difference at 11. So the new fraction is 3k over 4k with 4k minus 3k equal to 11, giving 33 over 44. Now subtract 8 from each.
Updated On: Jul 17, 2026
  • 25/26
  • 35/26
  • 26/35
  • 25/36
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The Correct Option is D

Solution and Explanation

Step 1: Put the fraction into one variable.
Let the numerator be \( n \). The denominator is 11 more than the numerator, so the denominator is \( n+11 \).
The fraction is therefore
\[ \frac{n}{n+11} \]
Using one variable rather than two is what keeps this to a single easy equation.

Step 2: Apply the second condition.
Adding 8 to both parts gives the new fraction
\[ \frac{n+8}{n+11+8} = \frac{n+8}{n+19} \]
We are told this equals \( \frac{3}{4} \), so
\[ \frac{n+8}{n+19} = \frac{3}{4} \]

Step 3: Cross multiply and solve.
\[ 4(n+8) = 3(n+19) \]
\[ 4n + 32 = 3n + 57 \]
Bring the \( n \) terms to the left and the numbers to the right:
\[ 4n - 3n = 57 - 32 \]
\[ n = 25 \]

Step 4: Build the fraction.
The numerator is 25 and the denominator is \( 25 + 11 = 36 \). So the fraction is
\[ \frac{25}{36} \]

Step 5: Verify against both conditions.
First condition: \( 36 - 25 = 11 \), so the denominator really is 11 more than the numerator.
Second condition: adding 8 to both gives \( \frac{33}{44} \), and dividing top and bottom by 11 gives \( \frac{3}{4} \). Both conditions hold, so the answer is confirmed.

Step 6: Test the other options quickly.
Option (A) 25/26: here the gap is only 1, not 11, so it fails at once.
Option (B) 35/26: the denominator is smaller than the numerator, so the gap is negative. It fails the first condition.
Option (C) 26/35: the gap is 9, not 11, and adding 8 gives \( \frac{34}{43} \), which is not \( \frac{3}{4} \).
Only 25/36 satisfies both statements in the question.

Final Answer:
The fraction is 25/36.
\[ \boxed{\frac{25}{36}} \]
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