Question

If 1 is subtracted from the numerator of a fraction it becomes (1/3) and if 5 is added to the denominator the fraction becomes (1/4). Which fraction shall result, if 1 is subtracted from the numerator and 5 is added to the denominator?

• A. $\frac{5}{12}$
• B. $\frac{7}{23}$
• C. $\frac{1}{8}$
• D. $\frac{2}{3}$
• E. None of these

Answer 1

The correct option is D $\frac{2}{3}$

Let the numerator and denominator of the fraction are x and y respectively,
$$\frac{x-1}{y}=\frac{1}{3}$$
3x-3=y
3x-y=3 .....(i)
and
$$\frac{x}{y+5}=\frac{1}{4}$$
4x-y=5 .....(ii)
On solving both the equations (i) and (ii), we get
x=2, y=3.