Question 114

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 . What is the fraction ?

Solution

Let the fraction be $$\frac{x}{y}$$

=> $$\frac{x+2}{y+2} = \frac{9}{11}$$

=> $$11x + 22 = 9y + 18$$

=> $$11x - 9y + 4 = 0$$

Also, $$\frac{x+3}{y+3} = \frac{5}{6}$$

=> $$6x + 18 = 5y + 15$$

=> $$6x - 5y + 3 = 0$$

Solving above equations, we get $$x = 7$$ and $$y = 9$$

=> Required fraction = $$\frac{7}{9}$$

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