Question

Numerator of a fraction is $5$ more than its denominator. If $4$ is added to numerator and denominator, the fraction obtained is $\frac{6}{5}$ . Find the fraction.

• A. $\frac{66}{11}$
• B. $\frac{26}{11}$
• C. $-\frac{26}{11}$
• D. $\frac{6}{11}$

Answer 1

The correct option is B $\frac{26}{11}$

given that numerator is 5 more than denomenator.

let denomenator be ${}^{\prime }{x}^{\prime }$

$\Rightarrow$ numerator $={}^{\prime \prime }x+5^{\prime \prime }$

fraction $=\frac{x+5}{5}$

4 is added to both numerator and denomenator

transformed fraction $\Rightarrow \frac{(x+5)+4}{x+4}\Rightarrow \frac{(x+9)}{(x+4)}$

$\Rightarrow \frac{6}{5}=\frac{x+9}{x+4}$

$\Rightarrow 6x+24=5x+45$

$\Rightarrow x=21$

$\therefore$ fraction $=\frac{x+5}{x}=\frac{21+5}{21}$

=$\frac{26}{21}$