The correct option is D None of the above
Let x be the numerator and y be the denominator.
Then, it is given that
(x+1)(y+1)=45;(x−5)(y−5)=12
(x+1)(y+1)=45⇒5x+5=4y+4⇒5x−4y+1=0….(1)
(x−5)(y−5)=12⇒2x−10=y−5⇒2x−y−5=0….(2)
Multiplying (2) by 4, we get
8x−4y−20=0…(3)
Subtracting (3) from (1), we get
−3x+21=0
⇒x=7
Putting x = 7 in (2), we get
2×7−y−5=0
⇒y=9
Therefore, the fraction is 79.