Let the number of boys appearing for admission be $x,$ therefore the number of girls appearing for admission be $2x.$
Then the total number of students $ = (x+2x) = 3x$
- The number of girls get admission $ = \frac{30}{100}\times2x = \frac{3x}{5}$
- The number of boys get admission $ = \frac{45}{100}\times x = \frac{9x}{20}$
The total number of students who get admission $ = \left(\frac{3x}{5} + \frac{9x}{20}\right) = \frac{21x}{20}$
- The number of girls who do not get admission $ = \left(2x-\frac{3x}{5}\right) = \frac{7x}{5}$
- The number of boys who do not get admission $ = \left(x-\frac{9x}{20}\right) = \frac{11x}{20}$
The total number of students who do not get admission $ = \left(3x – \frac{21x}{20}\right) = \frac{39x}{20}$
$$\text{(or)}$$
The total number of students who do not get admission $ = \frac{7x}{5} + \frac{11x}{20} = \frac{28x + 11x}{20} = \frac{39x}{20}$
$\therefore$ The percentage of candidates who do not get admission $ = \left(\dfrac{\frac{39x}{20}}{3x} \right)\times 100\% = \dfrac{13}{20} \times 100\% = 65 \%. $
$\textbf{Short Method:}$ Let the number of boys appearing for admission be $100,$ therefore the number of girls appearing for admission be $200.$
Then the total number of students $ = 100+200 = 300$
- The number of girls get admission $ = \frac{30}{100}\times 200 = 60$
- The number of boys get admission $ = \frac{45}{100}\times 100 = 45$
The total number of students who do not get admission $ = 300-(60+45) = 300-105 = 195$
$\therefore$ The percentage of candidates who do not get admission $ = \dfrac{195}{300} \times 100\% = 65\%.$
Correct Answer $:\text{D}$