Question:easy

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
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Work from the final fraction backwards.
After adding 8 to both parts the fraction equals $\frac{3}{4}$. Any fraction equal to $\frac{3}{4}$ can be written as $\frac{3k}{4k}$ for some number $k$. So
\[ \text{new numerator} = 3k, \qquad \text{new denominator} = 4k \]

Step 2: Use the gap, which addition never changes.
Adding the same 8 to the numerator and the denominator shifts both by the same amount, so the difference between them stays exactly what it was, namely 11. Applying this to the new fraction,
\[ 4k - 3k = 11 \]
\[ k = 11 \]
This is the neat trick of the question: the difference is an invariant.

Step 3: Recover the new fraction.
\[ \text{new numerator} = 3 \times 11 = 33, \qquad \text{new denominator} = 4 \times 11 = 44 \]
So the fraction after the change is $\frac{33}{44}$, which does reduce to $\frac{3}{4}$.

Step 4: Undo the addition.
Subtract the 8 that was added to each part:
\[ \text{original numerator} = 33 - 8 = 25 \]
\[ \text{original denominator} = 44 - 8 = 36 \]
So the original fraction is $\frac{25}{36}$, and its gap $36 - 25 = 11$ is exactly as stated.

Step 5: Screen the options against the gap rule alone.
The fastest filter is the difference of 11 between denominator and numerator.
For $\frac{25}{26}$ the difference is 1. Rejected.
For $\frac{35}{26}$ the difference is $-9$. Rejected.
For $\frac{26}{35}$ the difference is 9. Rejected.
For $\frac{25}{36}$ the difference is 11. Accepted, and it is the only one left, so no further testing is even needed.

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