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The sum of the numerator and denominator of the certain fractions is 8. If 2 is added to both the numerator and the denominator the value of the fraction increased by 4/35, then the fraction is:
- a)1/7
- b)3/5
- c)5/3
- d)Can not be determinted
Correct answer is option 'B'. Can you explain this answer?
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The sum of the numerator and denominator of the certain fractions is ...
Let fraction be x/y by given condition
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The sum of the numerator and denominator of the certain fractions is ...
Understanding the Problem
To solve the problem, we need to find a fraction where the sum of the numerator (let's call it x) and denominator (y) equals 8. This gives us the equation:
- x + y = 8
When we add 2 to both the numerator and the denominator, the value of the fraction increases by 4/35.
Setting Up the Equation
The initial fraction can be expressed as:
- Original fraction = x/y
After adding 2 to both, the new fraction becomes:
- New fraction = (x + 2)/(y + 2)
According to the problem, the change in value is:
- (x + 2)/(y + 2) - x/y = 4/35
Substituting the Values
From the first equation (x + y = 8), we can express y as:
- y = 8 - x
Substituting y into the change in value equation gives:
- (x + 2)/(10 - x) - x/(8 - x) = 4/35
Finding a Common Denominator
To simplify, find a common denominator for both fractions, which is (10 - x)(8 - x):
- (x + 2)(8 - x) - x(10 - x) = 4/35 * (10 - x)(8 - x)
Expanding this will yield a solvable equation.
Solving for x
Through algebraic manipulation, we will find possible values for x. After solving the equation, we find:
- x = 3 and y = 5 (since x + y = 8)
Thus, the fraction is:
- 3/5
Conclusion
The fraction that satisfies the given conditions is:
- Answer: 3/5 (Option B)
To solve the problem, we need to find a fraction where the sum of the numerator (let's call it x) and denominator (y) equals 8. This gives us the equation:
- x + y = 8
When we add 2 to both the numerator and the denominator, the value of the fraction increases by 4/35.
Setting Up the Equation
The initial fraction can be expressed as:
- Original fraction = x/y
After adding 2 to both, the new fraction becomes:
- New fraction = (x + 2)/(y + 2)
According to the problem, the change in value is:
- (x + 2)/(y + 2) - x/y = 4/35
Substituting the Values
From the first equation (x + y = 8), we can express y as:
- y = 8 - x
Substituting y into the change in value equation gives:
- (x + 2)/(10 - x) - x/(8 - x) = 4/35
Finding a Common Denominator
To simplify, find a common denominator for both fractions, which is (10 - x)(8 - x):
- (x + 2)(8 - x) - x(10 - x) = 4/35 * (10 - x)(8 - x)
Expanding this will yield a solvable equation.
Solving for x
Through algebraic manipulation, we will find possible values for x. After solving the equation, we find:
- x = 3 and y = 5 (since x + y = 8)
Thus, the fraction is:
- 3/5
Conclusion
The fraction that satisfies the given conditions is:
- Answer: 3/5 (Option B)
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The sum of the numerator and denominator of the certain fractions is 8. If 2 is added to both the numerator and the denominator the value of the fraction increased by 4/35, then the fraction is:a)1/7b)3/5c)5/3d)Can not be determintedCorrect answer is option 'B'. Can you explain this answer?
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