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.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 500
Let the Number of boys and Girls who appeared in the exam be a and b respectively,
So, according to the question
Number of boys passed in exam = [(100 - 20) × a ]/100 = 0.80a
Number of girls passed in exam = [(100-15) × b]/100 = 0.85b
Given condition (1)
0.80a = 0.85b + 70
0.80a - 0.85b =70 .....(i)
Given condition (2)
Total failed students = 90
= 0.20a +0.15b = 90 .....(ii)
From eqn (1) - [4 × eqn (ii)]
⇒ (-0.85b) - 0.60b = 70 - 360
⇒ 1.45b = 290
⇒ y = 200
Put this value in eqn (i)
⇒ 0.80a = 0.85 × 200 + 70
⇒ 0.80a = 170 + 70 = 240
⇒ a = 300
Total number of students appeared = 200 + 300 = 500