Question
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.
Solution
Let the Number of boys and Girls who appeared in exam be x and y respectively, So, according to question- Number of boys passed in exam = [(100 - 20) × x]/100 = 0.80x Number of girls passed in exam = [(100 - 15) × y]/100 = 0.85y Condition (1) - ⇒ 0.80x = 0.85y + 70 ⇒ 0.80x - 0.85y = 70 ...(i) Condition (2) - Total failed students = 90 ⇒ 0.20x + 0.15y = 90 ...(ii) From eqn (1) - [4 × eqn (ii)] ⇒ (-0.85y) - 0.60y = 70 - 360 ⇒ 1.45y = 290 ⇒ y = 200 Put this value in eqn (i) ⇒ 0.80x = 0.85 × 200 + 70 ⇒ 0.80x = 170 + 70 = 240 ⇒ x = 300 So, total number of students appeared in exam = 300 + 200 = 500.
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