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 denominator it becomes 5/6 . Find the fraction.
Answers
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Answer:
Let the numerator and denominator be x and y respectively.
Therefore, the required fraction will be x/y
According to Question now,
➳ (x + 2)/(y + 2) = 9/11
➳ 11(x + 2) = 9(y + 2)
➳ 11x + 22 = 9y + 18
➳ 22 - 18 = 9y - 11x
➳ 4 = 9y - 11x
➳ 11x = 9y - 4
➳ x = 9y - 4/11.......[Equation (i)]
Now, it is given that 3 is added to both numerator and denominator it becomes 5/6 :]
➳ (x + 3)/(y + 3) = 5/6
➳ (x + 3)6 = 5(y + 3)
➳ 6x + 18 = 5y + 15
➳ 6x - 5y + 18 - 15 = 0
➳ 6x - 5y + 3 = 0
➳ 6(9y - 4)/11 - 5y + 3 = 0
➳ 54y - 24/11 = 5y - 3
➳ 54y - 24 = 11(5y - 3)
➳ 54y - 24 = 55y - 33
➳ -24 + 33 = 55y - 54y
➳ 9 = y
Now, Putting y = 9 in equation (i) we get,
➳ x = 9y - 4/11
➳ x = 9(9) - 4/11
➳ x = 81 - 4/11
➳ x = 77/11
➳ x = 7
Therefore, the required fraction is 7/9.