A fraction becomes 1/2 when 1 is added to both its numerator and denominator. And it becomes 1/4 when 1 is subtracted from both the numerator and denominator. Find the fraction.

Question: A fraction becomes 1/2 when 1 is added to both its numerator and denominator, and it becomes 1/4 when 1 is subtracted from both the numerator and denominator. Find the fraction.

Solution:
Let the required fraction is x/y
Then,
(x + 1)/(y + 1) = 1/2
⇒ 2x + 2 = y + 1
∴ 2x - y = -1 ........(i)

And
(x - 1)/(y - 1) = 1/4
⇒ 4x - 4 = y - 1
⇒ 4x - y = 4 - 1
∴ 4x - y = 3 ........(ii)

Now,
Multiplying (i) by 2 then subtracting (ii) from (i) we get,
-2y + y = - 2 - 3
⇒ -y = - 5
∴ y = 5

Putting the value of y in (i) we get,
2x - 5 = - 1
⇒ 2x = - 1 + 5
⇒ 2x = 4
∴ x = 2

So, the required fraction = 2/5