Some students (boys and girls) from different schools appeared for an Olympiad exam. 20% of boys and 15% of girls failed. The number of boys who passed was 70 more than the number of girls who passed. A total of 90 students failed. Find the number of students who appeared.

Correct answer: 500. With B boys and G girls: 0.20B + 0.15G = 90 and 0.80B = 0.85G + 70. Solving gives B = 300 and G = 200, so the total is 500.

Background: Make two equations from the two facts and solve them.

• 350: 350 does not satisfy both conditions.
• 400: 400 does not satisfy both conditions.
• 450: 450 does not satisfy both conditions.

Did you know? Check: failed = 60 + 30 = 90; passed = 240 boys and 170 girls, a difference of 70.

Memory trick: Two facts → two equations.