The numerator of a fraction is 4 less than its denominator. If 1 is added to both the numerator and denominator, it becomes $\frac{1}{2}$ Find the fraction.

The correct answer is $\frac{3}{7}$

Let the numerator be x
∴ The denominator will be (x + 4)
We can write the equation as follows
$\frac{(x + 1)}{(x + 4 + 1)}$ = $\frac{1}{2}$
∴ By cross multiplying, we get
2 (x + 1) = 1 (x + 4 + 1)
or 2x + 2 = x + 4 + 1
∴ 2x - x = 5 - 2
∴ x = 3
∴ Numerator is 3 and the denominator is (3 + 4) = 7
The fraction is $\frac{3}{7}$