Question

The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1/3 of it. Find the original fraction.

Answer 1

n = d - 5

2n/(d + 16) = n/d - 1/3 n/d
2n/(d + 16) = 2/3 n/d Divide by 2n
1 / (d + 16) = 1/3 d
Here's the tricky part.
d + 16 = 3d the two denominators are equal. the numerators are both 1.
16 = 2d
d = 8
so the numerator is d - 5
n = 8 - 5
n = 3

Let's see if it checks out.
n = 3
d = 8

2*3 = 6
8 + 16 = 24
New fraction 6/24 = 1/4
(3/8 - 1/3 ) = 1/8
3/8 - 1/8 = 1/4 so it checks with the original conditions put on it.