Question : The ratio of the number of boys to girls in a school is 5 : 2. If 87% of the boys and 80% of the girls passed in the annual exams, then find the percentage of students who failed in the annual exams.
Option 1: 18%
Option 2: 16%
Option 3: 15%
Option 4: 17%
Correct Answer: 15%
Solution :
The ratio of boys and girls is 5 : 2.
Let us assume the total number of boys and girls is 500 and 200, respectively.
87% of the boys passed. So, 13% of boys failed.
Number of boys failed = $500 \times \frac{13}{100}$ = 65
80% of the girls passed. So, 20% of the girls failed.
Number of girls failed = $200 \times \frac{20}{100}$ = 40
Total number of students failed = (65 + 40) = 105
Total number of students in school = 500 + 200 = 700
$\therefore$ Percentage of failed students = $\frac{105}{700} \times 100$ = 15%
Hence, the correct answer is 15%.
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