The denominator of a fraction is 1 more than twice its numerator. If 1 is added to the numerator and the denominator, the ratio of the numerator to the denominator is 1:2. Find the fraction.
Let the numerator be x and denominator be y.
According to the first condition
y=2x+1
2x−y=−1 ...............(i)
According to the second condition
(x+1)(y+1)=12
⇒2(x+1)=1(y+1)
⇒2x+2=y+1
⇒2x−y=1−2
⇒2x−y=−1...............(ii)
From (i) and (ii) we have
There can be infinite values that will satisfy.
One such possible value is x=4 and y=9
∴, the fraction is 49