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If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction?
Most Upvoted Answer
If 2 is subtracted from the numerator and 1 is added to the denominato...
Explanation:

Given:
Let the original fraction be x/y.

Step 1: Forming the first equation
When 2 is subtracted from the numerator and 1 is added to the denominator, the fraction becomes (x-2)/(y+1).
According to the given condition, (x-2)/(y+1) = 1/2.
This gives us the first equation: (x-2)/(y+1) = 1/2.

Step 2: Forming the second equation
When 4 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes (x+4)/(y-3).
According to the given condition, (x+4)/(y-3) = 3/2.
This gives us the second equation: (x+4)/(y-3) = 3/2.

Step 3: Solving the equations
Solving the first equation, we get:
2(x-2) = y+1
2x - 4 = y + 1
2x = y + 5
y = 2x - 5
Substitute y = 2x - 5 into the second equation:
(x+4)/(2x-5-3) = 3/2
(x+4)/(2x-8) = 3/2
2(x+4) = 3(2x-8)
2x + 8 = 6x - 24
32 = 4x
x = 8
Substitute x = 8 into y = 2x - 5:
y = 2(8) - 5
y = 16 - 5
y = 11
Therefore, the fraction is 8/11.
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If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction?
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