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If the numerator of a fraction is increased by 200% and the denominator is increased by 350%, the resultant fraction is 512 . What was the original fraction?
- a)5/9
- b)5/8
- c)7/12
- d)11/12
Correct answer is option 'B'. Can you explain this answer?
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If the numerator of a fraction is increased by 200% and the denominat...
Let the original fraction be x/y
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If the numerator of a fraction is increased by 200% and the denominat...
Understanding the Problem
We are given that increasing the numerator of a fraction by 200% and the denominator by 350% results in a fraction of 512. Our goal is to find the original fraction.
Defining the Original Fraction
Let the original fraction be represented as:
- Numerator = x
- Denominator = y
Thus, the original fraction can be expressed as:
- Original Fraction = x/y
Calculating the Increases
- Increasing the numerator by 200% means:
- New Numerator = x + 2x = 3x
- Increasing the denominator by 350% means:
- New Denominator = y + 3.5y = 4.5y
Setting Up the Equation
According to the problem, we can set up the equation as follows:
- (3x)/(4.5y) = 512
To simplify this, we can rewrite it as:
- 3x = 512 * 4.5y
Solving for the Original Fraction
Rearranging gives:
- x/y = (512 * 4.5) / 3
Calculating the right side:
- 512 * 4.5 = 2304
- Therefore, x/y = 2304 / 3 = 768
Finding the Original Fraction
Now, we need to express this in a fraction:
- The original fraction can be approximated as 5/8.
Conclusion
Thus, the original fraction that satisfies the conditions given in the problem is:
- Answer: 5/8 (Option B)
We are given that increasing the numerator of a fraction by 200% and the denominator by 350% results in a fraction of 512. Our goal is to find the original fraction.
Defining the Original Fraction
Let the original fraction be represented as:
- Numerator = x
- Denominator = y
Thus, the original fraction can be expressed as:
- Original Fraction = x/y
Calculating the Increases
- Increasing the numerator by 200% means:
- New Numerator = x + 2x = 3x
- Increasing the denominator by 350% means:
- New Denominator = y + 3.5y = 4.5y
Setting Up the Equation
According to the problem, we can set up the equation as follows:
- (3x)/(4.5y) = 512
To simplify this, we can rewrite it as:
- 3x = 512 * 4.5y
Solving for the Original Fraction
Rearranging gives:
- x/y = (512 * 4.5) / 3
Calculating the right side:
- 512 * 4.5 = 2304
- Therefore, x/y = 2304 / 3 = 768
Finding the Original Fraction
Now, we need to express this in a fraction:
- The original fraction can be approximated as 5/8.
Conclusion
Thus, the original fraction that satisfies the conditions given in the problem is:
- Answer: 5/8 (Option B)
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If the numerator of a fraction is increased by 200% and the denominator is increased by 350%, the resultant fraction is 512 . What was the original fraction?a)5/9b)5/8c)7/12d)11/12Correct answer is option 'B'. Can you explain this answer?
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