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If 4 is added to the numerator of a fraction it becomes 1/3 and if 3 is added to the denominator it becomes 1/6 then find the numerator and denominator is
- a)5/26
- b)25/4
- c)6/17
- d)5/27
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If 4 is added to the numerator of a fraction it becomes 1/3 and if 3 i...
Let the numerator be x and denominator be y
Fraction will be x/y
According to the question
(x + 4)/y = 1/3
⇒ 3x + 12 = y ......(1)
Now,
x/(y + 3) = 1/6
⇒ 6x = y + 3 ......(2)
Solving both the equations we get
x = 5 and y = 27
So , fraction x/y = 5/27
Most Upvoted Answer
If 4 is added to the numerator of a fraction it becomes 1/3 and if 3 i...
Given information:
- Adding 4 to the numerator of a fraction gives 1/3.
- Adding 3 to the denominator of the same fraction gives 1/6.
Let's start by setting up equations to represent the given information:
- (numerator + 4) / denominator = 1/3
- numerator / (denominator + 3) = 1/6
We can simplify these equations by cross-multiplying and solving for the numerator and denominator separately.
- 3(numerator + 4) = denominator
- 6numerator = denominator + 3
Now we have two equations with two variables (numerator and denominator). We can use substitution or elimination to solve for these variables.
Using substitution:
- From the first equation, denominator = 3(numerator + 4)
- Substitute this into the second equation: 6numerator = 3(numerator + 4) + 3
- Simplifying: 3numerator = 15
- Solving for numerator: numerator = 5
Now we can substitute this value back into either of the original equations to find the denominator:
- From the first equation: 3(numerator + 4) = denominator
- Substituting numerator = 5: 3(5 + 4) = denominator
- Simplifying: denominator = 27
Therefore, the fraction is 5/27. The correct answer is option D.
- Adding 4 to the numerator of a fraction gives 1/3.
- Adding 3 to the denominator of the same fraction gives 1/6.
Let's start by setting up equations to represent the given information:
- (numerator + 4) / denominator = 1/3
- numerator / (denominator + 3) = 1/6
We can simplify these equations by cross-multiplying and solving for the numerator and denominator separately.
- 3(numerator + 4) = denominator
- 6numerator = denominator + 3
Now we have two equations with two variables (numerator and denominator). We can use substitution or elimination to solve for these variables.
Using substitution:
- From the first equation, denominator = 3(numerator + 4)
- Substitute this into the second equation: 6numerator = 3(numerator + 4) + 3
- Simplifying: 3numerator = 15
- Solving for numerator: numerator = 5
Now we can substitute this value back into either of the original equations to find the denominator:
- From the first equation: 3(numerator + 4) = denominator
- Substituting numerator = 5: 3(5 + 4) = denominator
- Simplifying: denominator = 27
Therefore, the fraction is 5/27. The correct answer is option D.
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Community Answer
If 4 is added to the numerator of a fraction it becomes 1/3 and if 3 i...
5/27 = 9/27 = 1/3
5/30 = 1/6
5/30 = 1/6
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