CAT 2017Slot 1QAQuestion & Solution
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
Options
35
50
60
65
Solution
1. Concept Used
- Topic: Percentage — Weighted Average of Groups
- Formula: $$\text{Percentage not admitted} = \frac{\text{Total candidates} - \text{Total admitted}}{\text{Total candidates}} \times 100$$
2. Calculation
Let the number of boys = $x$, so the number of girls = $2x$ (since girls are twice the boys). The total number of candidates = $x + 2x = 3x$.
Number of girls getting admission = $30%$ of $2x = \frac{30}{100} \times 2x = 0.6x$
Number of boys getting admission = $45%$ of $x = \frac{45}{100} \times x = 0.45x$
Total candidates getting admission = $0.6x + 0.45x = 1.05x$
Total candidates not getting admission = $3x - 1.05x = 1.95x$
Percentage of candidates not getting admission: $$\frac{1.95x}{3x} \times 100 = \frac{1.95}{3} \times 100 = 0.65 \times 100 = 65%$$
3. Solution
Answer = Option D ✅
The percentage of candidates who do not get admission is 65%.