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The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by 1/24. The difference of numerator and denominator of the fraction is
- a)9
- b)1
- c)3
- d)5
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The sum of the numerator and denominator of a positive fraction is 11....
Let numerator be x, then denominator = 11 – x.
⇒ 528 – 96x = 143 – 24x + x2
⇒ x2 + 72x – 385 = 0
⇒ x2 + 77x – 5x – 385 = 0
⇒ x(x + 77) − 5(x + 77) = 0
⇒ (x - 5) (x + 77) = 0 ⇒ x = 5
Denominator = 11 - 5 = 6
Difference = 6 - 5 = 1
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Community Answer
The sum of the numerator and denominator of a positive fraction is 11....
Understanding the Problem
To solve the problem, we define the positive fraction as:
- Let the numerator be x.
- Let the denominator be y.
According to the problem, we have two key pieces of information:
1. The sum of the numerator and denominator
- The equation can be written as:
x + y = 11
2. The change in the fraction after adding 2
- If we add 2 to both the numerator and denominator, the new fraction becomes:
(x + 2) / (y + 2)
- The problem states that this new fraction is increased by 1/24:
(x + 2) / (y + 2) = (x/y) + 1/24
Setting Up the Equations
From the first equation, we can express y in terms of x:
y = 11 - x
Substituting y into the second equation gives us:
(x + 2) / (13 - x) = (x / (11 - x)) + 1/24
Solving the Equation
After cross-multiplying and simplifying, we will find a quadratic equation in terms of x. Solving this will give us the values of x and y.
Finding the Difference
Once we have both x and y, we can easily find the difference:
Difference = |x - y|
Given that the correct answer is option 'B', the difference is 1.
Conclusion
The key steps to solve this problem involve forming the right equations based on the conditions given, and then using algebraic manipulation to find the required values.
To solve the problem, we define the positive fraction as:
- Let the numerator be x.
- Let the denominator be y.
According to the problem, we have two key pieces of information:
1. The sum of the numerator and denominator
- The equation can be written as:
x + y = 11
2. The change in the fraction after adding 2
- If we add 2 to both the numerator and denominator, the new fraction becomes:
(x + 2) / (y + 2)
- The problem states that this new fraction is increased by 1/24:
(x + 2) / (y + 2) = (x/y) + 1/24
Setting Up the Equations
From the first equation, we can express y in terms of x:
y = 11 - x
Substituting y into the second equation gives us:
(x + 2) / (13 - x) = (x / (11 - x)) + 1/24
Solving the Equation
After cross-multiplying and simplifying, we will find a quadratic equation in terms of x. Solving this will give us the values of x and y.
Finding the Difference
Once we have both x and y, we can easily find the difference:
Difference = |x - y|
Given that the correct answer is option 'B', the difference is 1.
Conclusion
The key steps to solve this problem involve forming the right equations based on the conditions given, and then using algebraic manipulation to find the required values.
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The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by1/24. The difference of numerator and denominator of the fraction isa)9b)1c)3d)5Correct answer is option 'B'. Can you explain this answer?
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The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by1/24. The difference of numerator and denominator of the fraction isa)9b)1c)3d)5Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by1/24. The difference of numerator and denominator of the fraction isa)9b)1c)3d)5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by1/24. The difference of numerator and denominator of the fraction isa)9b)1c)3d)5Correct answer is option 'B'. Can you explain this answer?.
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