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The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. What is the fraction?
- a)2/7
- b)3/7
- c)5/7
- d)1/7
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The sum of the numerator and denominator of a fraction is 12. If the d...
Let the fraction be x/y
then x + y = 12 .....(1)
and
By solving eqn (1) and (2), we get x = 5, y = 7
x/y = 5/7
then x + y = 12 .....(1)
and
By solving eqn (1) and (2), we get x = 5, y = 7
x/y = 5/7
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The sum of the numerator and denominator of a fraction is 12. If the d...
Understanding the Problem
To solve the problem, we need to define the fraction and use the information given in the question.
Step 1: Define Variables
- Let the numerator be represented as "x".
- Let the denominator be represented as "y".
Step 2: Set Up Equations
From the problem statement, we have two key pieces of information:
1. The sum of the numerator and denominator is 12:
- Equation 1: x + y = 12
2. If the denominator is increased by 3, the fraction becomes 1/2:
- Equation 2: x / (y + 3) = 1/2
Step 3: Solve the Equations
From Equation 1, we can express y in terms of x:
- y = 12 - x
Now, substitute y into Equation 2:
- x / (12 - x + 3) = 1/2
- This simplifies to: x / (15 - x) = 1/2
Cross-multiplying gives:
- 2x = 15 - x
- Adding x to both sides: 3x = 15
- Thus, x = 5.
Now, substitute x back into Equation 1 to find y:
- y = 12 - 5 = 7.
Step 4: Identify the Fraction
Now we have:
- Numerator (x) = 5
- Denominator (y) = 7
Therefore, the fraction is:
- 5/7.
Conclusion
The correct answer is option 'C': 5/7. This satisfies both conditions of the problem, confirming our solution.
To solve the problem, we need to define the fraction and use the information given in the question.
Step 1: Define Variables
- Let the numerator be represented as "x".
- Let the denominator be represented as "y".
Step 2: Set Up Equations
From the problem statement, we have two key pieces of information:
1. The sum of the numerator and denominator is 12:
- Equation 1: x + y = 12
2. If the denominator is increased by 3, the fraction becomes 1/2:
- Equation 2: x / (y + 3) = 1/2
Step 3: Solve the Equations
From Equation 1, we can express y in terms of x:
- y = 12 - x
Now, substitute y into Equation 2:
- x / (12 - x + 3) = 1/2
- This simplifies to: x / (15 - x) = 1/2
Cross-multiplying gives:
- 2x = 15 - x
- Adding x to both sides: 3x = 15
- Thus, x = 5.
Now, substitute x back into Equation 1 to find y:
- y = 12 - 5 = 7.
Step 4: Identify the Fraction
Now we have:
- Numerator (x) = 5
- Denominator (y) = 7
Therefore, the fraction is:
- 5/7.
Conclusion
The correct answer is option 'C': 5/7. This satisfies both conditions of the problem, confirming our solution.
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