Question

The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent with $\frac{1}{2}$. Find the fraction.

Answer 1

Let's assume the numerator of the fraction to be x.
So,
Denominator = x + 12
The fraction = $\frac{x}{x+12}$
Now, from the given information we have
$\frac{x-2}{x+12+7}=\frac{1}{2}$
On cross multiplying.
2 (x - 2) = (x + 12 + 7)
2x - 4 = x + 19
2x - x = 19 + 4
x = 23
Hence, the numerator of the fraction is 23 and the denominator of the fraction is (23 + 12) = 35.
Therefore, the fraction is $\frac{23}{35}$