Question

The denominator of a fraction is greater than the numerator by 8. When the numerator is increased by 17 and the denominator is decreased by 1, the fraction obtained is $\frac{3}{2}$. What was the original fraction?

• A. $\frac{11}{19}$
• B. $\frac{13}{21}$
• C. $\frac{10}{18}$
• D. $\frac{9}{17}$

Answer 1

The correct option is B $\frac{13}{21}$

Let the numerator be N and the denominator be D.

Now, we know that the denominator is greater than the numerator by 8.
Hence, $D=N+8$.

Now, when denominator is decreased by 1, we obtain the expression $D-1=N+8-1=N+7$.

Now, the fraction obtained when the numerator is increased by 17 and the denominator is decreased by 1 is $\frac{3}{2}$.

Hence, $\frac{N+17}{N+7}=\frac{3}{2}$

$\Rightarrow 2(N+17)=3(N+7)$
$\Rightarrow 2N+34=3N+21$
$\Rightarrow N=13$
Now, $D=N+8=13+8=21$
Hence the fraction is $\frac{N}{D}=\frac{13}{21}$.