Question

a fraction becomes 9/11,if 2is added to both the numerator and denomonator .if 3is added to both the numerator and denominator it becomes 5/6 find fraction

Answer 1

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

Case - (i)
A fraction becomes 9/11,if 2 is added to both the numerator and denomonator.
$\frac{x+2}{y+2}$ = $\frac{9}{11}$
11(x+2) = 9(y+2)
11x+22 = 9y+18
11x-9y = 18-22
11x - 9y = -4 -------(1)

Case - (ii)
If 3 is added to both the numerator and denominator it becomes 5/6.
$\frac{x+3}{y+3}$ = $\frac{5}6$
6(x+3) = 5(y+3)
6x+18 = 5y+15
6x-5y = 15-18
6x-5y = -3 --------(2)

Multiply equation (1) by 6 and equation (2) by 11, we get

66x - 54y = -24
66x - 55y = -33
----------------------
y = 9

Put y = 9 in equation (1)

11x - 9(9) = -4
11x - 81 = -4
11x = -4+81
11x = 77
x = 77/11
x = 7

Therefore, the fraction is $\frac{7}9$

Answer 2

f=x/y

x+2/y+2=9/11
11x+4/9=y
....
.....
6x+3/5=y..
.. solved the equation..
....f=7/9