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The denominator of a fraction is greater than its numerator by 25. If 7 is added to both in numerator and the denominator, it becomes 1/2. The fraction is 
  • a)
    29/54 
  • b)
    25/50 
  • c)
    18/43 
  • d)
    7/32
Correct answer is option 'C'. Can you explain this answer?
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Given information:
- The denominator of a fraction is greater than its numerator by 25.
- If 7 is added to both the numerator and the denominator, it becomes 1/2.

Let's solve the problem step by step:

Step 1: Set up the equation based on the given information:
Let the numerator of the fraction be x.
Then, the denominator of the fraction will be x + 25.
So, the fraction can be represented as x/(x + 25).
Adding 7 to both the numerator and the denominator gives us the new fraction (x + 7)/(x + 25 + 7) = (x + 7)/(x + 32) = 1/2.

Step 2: Solve the equation:
Now, we have the equation (x + 7)/(x + 32) = 1/2.
Cross multiply to get: 2(x + 7) = x + 32.
Simplify: 2x + 14 = x + 32.
Rearrange: 2x - x = 32 - 14.
Solve: x = 18.

Step 3: Find the fraction:
The numerator is 18 and the denominator is 18 + 25 = 43.
Therefore, the fraction is 18/43.

Final answer: The fraction is 18/43. Hence, option (c) is correct.
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