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A fraction becomes 1/3 when 1 is subtracted from its numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction
- a)4/12
- b)3/13
- c)5/12
- d)11/7
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A fraction becomes 1/3 when 1 is subtracted from its numerator and it ...
Given:
- A fraction becomes 1/3 when 1 is subtracted from its numerator.
- It becomes 1/4 when 8 is added to its denominator.
To find:
The fraction that satisfies both conditions.
Solution:
Let's assume the fraction is represented as x/y.
According to the first condition, when 1 is subtracted from the numerator, the fraction becomes 1/3. This can be written as:
(x - 1)/y = 1/3
Multiplying both sides of the equation by y, we get:
(x - 1) = (y/3) ........(1)
According to the second condition, when 8 is added to the denominator, the fraction becomes 1/4. This can be written as:
x/(y + 8) = 1/4
Multiplying both sides of the equation by (y + 8), we get:
x = (y + 8)/4 ........(2)
Now, we have two equations (1) and (2) with two variables (x and y). We can solve these equations to find the values of x and y.
Let's substitute the value of x from equation (2) into equation (1):
((y + 8)/4 - 1) = (y/3)
Multiplying both sides of the equation by 12 to eliminate the fractions, we get:
3(y + 8) - 12 = 4y
3y + 24 - 12 = 4y
3y - 4y = 12 - 24
-y = -12
y = 12
Substituting the value of y back into equation (2), we can find the value of x:
x = (12 + 8)/4
x = 20/4
x = 5
Therefore, the fraction is 5/12, which is option C.
- A fraction becomes 1/3 when 1 is subtracted from its numerator.
- It becomes 1/4 when 8 is added to its denominator.
To find:
The fraction that satisfies both conditions.
Solution:
Let's assume the fraction is represented as x/y.
According to the first condition, when 1 is subtracted from the numerator, the fraction becomes 1/3. This can be written as:
(x - 1)/y = 1/3
Multiplying both sides of the equation by y, we get:
(x - 1) = (y/3) ........(1)
According to the second condition, when 8 is added to the denominator, the fraction becomes 1/4. This can be written as:
x/(y + 8) = 1/4
Multiplying both sides of the equation by (y + 8), we get:
x = (y + 8)/4 ........(2)
Now, we have two equations (1) and (2) with two variables (x and y). We can solve these equations to find the values of x and y.
Let's substitute the value of x from equation (2) into equation (1):
((y + 8)/4 - 1) = (y/3)
Multiplying both sides of the equation by 12 to eliminate the fractions, we get:
3(y + 8) - 12 = 4y
3y + 24 - 12 = 4y
3y - 4y = 12 - 24
-y = -12
y = 12
Substituting the value of y back into equation (2), we can find the value of x:
x = (12 + 8)/4
x = 20/4
x = 5
Therefore, the fraction is 5/12, which is option C.
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Community Answer
A fraction becomes 1/3 when 1 is subtracted from its numerator and it ...
Correct answer is C 5/12 because the denominator has 4+8=12
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A fraction becomes 1/3 when 1 is subtracted from its numerator and it becomes 1/4 when 8 is added to its denominator. Find the fractiona)4/12b)3/13c)5/12d)11/7Correct answer is option 'C'. Can you explain this answer?
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