Question

Students from various schools participated in a state-level olympiad.

1500 students from School A participated in the exam. The ratio of the boys to the girls was 7:8. 40% of the boys failed, while 70% of the girls passed in the exam from School A.

If the total number of students who failed from School A constitutes 10% of the total students who participated, find the number of students that participated in the olympiad.

• A. 5200
• B. 8000
• C. 9800
• D. 15000

Answer 1

The correct option is A 5200

Total number of students from School A = 1500
Ratio of boys and girls = 7:8

$\text{So, number of boys}=\frac{7}{15}\times 1500=700$

Number of girls = 1500 – 700 = 800

Number of students from School A who failed:

Boys:
$\text{40\% of 700}=\frac{40}{100}\times 700=280$

Girls:
We know that 70% of the girls passed, so 30% (100 – 70) of the girls failed in the exam.

$\text{30\% of 800}=\frac{30}{100}\times 800=240$

Total number of students who failed = 280 + 240 = 520

520 = 10% of the students who participated
x = 100% of the students who participated

Total number of students who participated in the olympiad =
$\frac{520}{10}\times 100=5200\text{students}$

Thus, a total of 5200 students participated in the olympiad.