a fraction becomes 9/11 ,if 2 is added to both the numerator and denominator. if 3 is added to both numerator and denominator it becomes 5/6.find the fraction.
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Let the fraction be x/y.
ACCORDING TO QUESTION
x+2 / y+2 = 11/9 _1
x+3 / y+3 = 5/6 _2
On solving further equation 1st we get
11(x + 2) = 9(y + 2)
11x + 22 = 9y + 18
11x - 9y + 4 = 0 _3
On sloving further equation 2nd we get
6(x + 3) = 5(x + 3)
6x + 18 = 5y + 15
6x - 5y + 3 = 0 _4
By elimination method in equation 3 and 4 we get the value of x and y
5(11x - 9y + 4 = 0)
9(6x - 5y + 3 = 0)
55x - 45y +20 = 0
54x - 45y + 27 = 0
On changing the sign and elimination we get
- x = - 7
x = 7
On putting the value of x in any of the above equation we get
y = 9
So the fraction will be :-
x/y = 7/9
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