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The sum of the numerator and denominator of the certain fraction 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 determined
Correct answer is option 'B'. Can you explain this answer?
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The sum of the numerator and denominator of the certain fraction is 8...
Let fraction be x/y by given condition
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We cant take 28 , taking y=5,x will become 3
Therefore x/y = ⅗
Most Upvoted Answer
The sum of the numerator and denominator of the certain fraction is 8...
Understanding the Problem
The problem involves finding a fraction where the sum of the numerator and denominator is 8, and modifying both by adding 2 changes its value by 4/35.
Let’s Define the Fraction
- Let the numerator be \( x \).
- Then the denominator is \( 8 - x \) (since their sum is 8).
Thus, the fraction can be represented as:
\[ \frac{x}{8 - x} \]
Applying the Condition
When 2 is added to both the numerator and denominator, the new fraction becomes:
\[ \frac{x + 2}{(8 - x) + 2} = \frac{x + 2}{10 - x} \]
According to the problem, this new fraction is equal to the original fraction plus \( \frac{4}{35} \):
\[ \frac{x + 2}{10 - x} = \frac{x}{8 - x} + \frac{4}{35} \]
Cross Multiplying
To eliminate the fractions, cross-multiply:
\[ (x + 2)(8 - x + 4/35(10 - x)) = x(10 - x) \]
This leads to a more complex equation, but we can simplify our approach.
Simplifying the Equation
We can directly substitute possible values for \( x \) since \( x \) and \( 8 - x \) must be positive integers.
Trying \( x = 3 \):
- Numerator: \( 3 \)
- Denominator: \( 5 \)
- Original fraction: \( \frac{3}{5} \)
Now, add 2 to both:
- New numerator: \( 5 \)
- New denominator: \( 7 \)
- New fraction: \( \frac{5}{7} \)
Calculate the increase:
\[ \frac{5}{7} - \frac{3}{5} = \frac{25 - 21}{35} = \frac{4}{35} \]
Conclusion
This confirms the calculations, leading us to conclude that the fraction is:
\[ \frac{3}{5} \]
Thus, the correct answer is option 'B'.
The problem involves finding a fraction where the sum of the numerator and denominator is 8, and modifying both by adding 2 changes its value by 4/35.
Let’s Define the Fraction
- Let the numerator be \( x \).
- Then the denominator is \( 8 - x \) (since their sum is 8).
Thus, the fraction can be represented as:
\[ \frac{x}{8 - x} \]
Applying the Condition
When 2 is added to both the numerator and denominator, the new fraction becomes:
\[ \frac{x + 2}{(8 - x) + 2} = \frac{x + 2}{10 - x} \]
According to the problem, this new fraction is equal to the original fraction plus \( \frac{4}{35} \):
\[ \frac{x + 2}{10 - x} = \frac{x}{8 - x} + \frac{4}{35} \]
Cross Multiplying
To eliminate the fractions, cross-multiply:
\[ (x + 2)(8 - x + 4/35(10 - x)) = x(10 - x) \]
This leads to a more complex equation, but we can simplify our approach.
Simplifying the Equation
We can directly substitute possible values for \( x \) since \( x \) and \( 8 - x \) must be positive integers.
Trying \( x = 3 \):
- Numerator: \( 3 \)
- Denominator: \( 5 \)
- Original fraction: \( \frac{3}{5} \)
Now, add 2 to both:
- New numerator: \( 5 \)
- New denominator: \( 7 \)
- New fraction: \( \frac{5}{7} \)
Calculate the increase:
\[ \frac{5}{7} - \frac{3}{5} = \frac{25 - 21}{35} = \frac{4}{35} \]
Conclusion
This confirms the calculations, leading us to conclude that the fraction is:
\[ \frac{3}{5} \]
Thus, the correct answer is option 'B'.
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The sum of the numerator and denominator of the certain fraction 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 determinedCorrect answer is option 'B'. Can you explain this answer?
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