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

A. 420

B. 400

C. 500

D. 350

Answer: Option C

Solution(By Examveda Team)

Let number of boys = B and number of girls = G
According to the question,
B × 80% - G × 85% = 70
⇒ 80B - 85G = 7000 . . . . . . (i)
Again,
B × 20% + G × 15% = 90
⇒ 20B + 15G = 9000
⇒ 80B + 60G = 36000 . . . . . . (ii)
From equation (i) - (ii)
145G = 29000
⇒ G = 200
20B + 15 × 200 = 9000
⇒ 20B = 6000
⇒ B = 300
∴ Total students = 300 + 200 = 500