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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.
Dear StudentHere is the required solution:Let the fraction be x/y.According to the question,(x+2) /(y+2) = 9/1111x + 22 = 9y + 1811x – 9y = -4 …………….. (1)(x+3) /(y+3) = 5/66x + 18 = 5y +156x – 5y = -3 ………………. (2)From (1),we getx = (-4+9y)/11 …………….. (3)Substituting the value of x in (2),we get6(-4+9y)/11 -5y = -3-24 + 54y – 55y = -33-y = -9y = 9 ………………… (4)Substituting the value of y in (3),we getx = (-4+9×9 )/11 = 7Hence the fraction is 7/9.Thanks
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