Question

In a given fraction, if five is subtracted from the numerator, the fraction becomes $\frac{1}{3}$ If one is subtracted from the denominator, the fraction becomes $\frac{1}{2}$ . What is the fraction?

• A. $\frac{14}{27}$
• B. $\frac{15}{31}$
• C. $\frac{17}{32}$
• D. $\frac{16}{33}$

Answer 1

The correct option is D $\frac{16}{33}$

Let the fraction be $\frac{x}{y}$

$\frac{x-5}{y}=\frac{1}{3}$

$3x-15=y.....\left(1\right)$

$\frac{x}{y-1}=\frac{1}{2}$

$2x=y-1$

$2x+1=y$ .... (2)

from (1) and (2), we get

$3x-15=2x+1$

$3x-2x=15+1$

$x=16$

$y=2\left(16\right)+1$ (from(2))

$=32+1=33.$

Hence the fraction is $\frac{16}{33}$