CAT 2017 Set-1 | Question: 75

Question

The number of girls appearing for an admission test is twice the number of boys. If $30\%$ of the girls and $45\%$ of the boys get admission, the percentage of candidates who do not get admission is

• A. $35$
• B. $50$
• C. $60$
• D. $65$

Answer 1

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 \%. $

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$\textbf{Short Method:}$ 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 $:\text{D}$