Question

(v) 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\6Find the
fraction.​

Answer 1

Let the fraction be x/y.

(x+2)/(y+2) = 9/11, or

9y+18 = 11x+22

9y = 11x+4, or

45y = 55x+20 …(1)

(x+3)/(y+3) = 5/6, or

5y+15 = 6x+18, or

5y = 6x+3, or

45y = 54x+27 …(2)

Equate (1) and (2)

55x+20 = 54x+27

x = 7

Again, 9y = 11x+4, or

9y = 77 + 4 or

y = 81/9 = 9

The fraction is (7/9).