A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
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Let the fraction be x/y.
According to the question,
(x + 2)/(y + 2) = 9/11
11x + 22 = 9y + 18
11x – 9y = -4 …………….. (1)
(x + 3)/(y + 3) = 5/6
6x + 18 = 5y +15
6x – 5y = -3 ………………. (2)
From (1), we get
x = (-4 + 9y)/11 …………….. (3)
Substituting the value of x in (2), we get
6[(-4 + 9y)/11] – 5y = -3
-24 + 54y – 55y = -33
-y = -9
y = 9 ………………… (4)
Substituting the value of y in (3), we get
x = (-4 + 81)/11 = 77/11 = 7
Hence, the fraction is 7/9.
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