SSC CGL Exam > SSC CGL Questions > The sum of the numerator and denominator of a...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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
Free Test
FREE
| Start Free Test |
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.
Attention SSC CGL Students!
To make sure you are not studying endlessly, EduRev has designed SSC CGL study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in SSC CGL.
|
Explore Courses for SSC CGL exam
|
|
Similar SSC CGL Doubts
Top Courses for SSC CGLView all
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?
Question Description
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for SSC CGL.
Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice SSC CGL tests.
|
|
Explore Courses for SSC CGL exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup