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Fraction becomes 9/11, If 2 is Added to Both the Numerator and Denominator. If 3 is Added to Both the Numerator and the Denominator, it Becomes 5/6. Find the Fraction. | Bzziii.com

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A fraction becomes `9/11`, if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and the denominator, it becomes `5/6`. Find the fraction. SOLUTION Let Numerator be x & Denominator be y So, Fraction is = `x/y` Given that, If 2 is added to both the numerators and denominator, fraction becomes `9/11` `"Numerators + 2"/"Denominator + 2"`= `9/11` `"x+ 2"/"y + 2"`= `9/11` 11 (`x + 2`) = 9 (`y + 2`) 11`x` + 22 = 9`y` + 18 11`x` - 9`y` = 11 - 22 11`x` - 9`y` = -4 .......(1) Also, Given that if 3 is added to both the numerator and the denominator, fraction become `5/6` `"Numerators + 3"/"Denominator + 3"`= `5/6` `"x+ 3"/"y + 3"`= `5/6` 6 (`x + 3`) = 5 (`y + 3`) 6`x` + 18 = 5`y` + 15 6`x` - 5`y` = 15 - 18 6`x` - 5`y` = - 3 .......(2) Hence, our equations are 11`x` - 9`y` = -4 .......(1) 6`x` - 5`y` = - 3 .......(2) From equation (1...
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