Question

The ratio of the numerator to the denominator of a certain fraction is one to four. If three is added to the numerator and

subtracted from the denominator, the new fraction reduces to one-third. What is the original fraction?
A 12/45
B 15/45
C 12/48

Answer 1

C 12/48

Explanation:

Original fraction:

x/y

The ratio of the numerator to the denominator is 1:4, so

x/y = 1/4

Cross multiply:

y = 4x

If three is added to the numerator and subtracted from the denominator, the new fraction reduces to one-third.

(x + 3)/(y - 3) = 1/3

Cross multiply:

3(x + 3) = 1(y - 3)

3x + 9 = y - 3

Above, we have y = 4x, so substitute 4x for y in the equation just above and solve for x.

3x + 9 = 4x - 3

12 = x

x = 12

y = 4(12) = 48

The original fraction is x/y = 12/48