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

$35$

$50$

$60$

$65$

✅ Correct Option: 4

We have an admission test where:

Girls appearing = 2 × Boys appearing

30% of girls get admission

45% of boys get admission

We need to find what percentage of all candidates don't get admission

Let's say the number of boys appearing = b

Then:

Number of girls appearing = 2b (given that girls are twice the boys)

Total candidates = boys + girls = b + 2b = 3b

Using variables makes calculations cleaner and we can work with any actual number of boys.

Boys who get admission:

45% of b = $\dfrac{45}{100} \times b = 0.45b$

Girls who get admission:

30% of 2b = $\dfrac{30}{100} \times 2b = 0.60b$

Total who get admission:

0.45b + 0.60b = 1.05b

Percentage of candidates who get admission:

$\dfrac{\text{Total who get admission}}{\text{Total candidates}} \times 100\%$

$= \dfrac{1.05b}{3b} \times 100\%$

Notice how 'b' cancels out - this confirms our variable approach works regardless of the actual number!

$= \dfrac{1.05}{3} \times 100\% = 0.35 \times 100\% = 35\%$

If 35% of candidates get admission then:

Percentage who don't get admission = 100% - 35% = 65%

Key Insight: This problem tests your ability to work with weighted averages. Since there are more girls than boys (2:1 ratio) the overall admission percentage is closer to the girls' rate (30%) than the boys' rate (45%).

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

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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