Correct answer is : 87%
Given,
Ratio of boys and girls = 5:3
Let ‘p’ and ‘q’ be the number of boys and girls respectively.
Hence, p/q = 5/3 ----(A)
Percentage of boys failed in exam is 16%.
Number of boys failed in exam
= 16% of p
= (16/100) x p
= 16p/100
Percentage of girls failed in exam is 8%.
Number of girls failed in exam
= 8% of q
= (8/100) x q
= 8q/100
Percentage of boys passed in exam
= (100 - 16)%
= 84%
Number of boys passed in exam
= 84% of p
= (84/100) x p
= 84p/100 -----(1)
Percentage of girls passed in exam
= (100 - 8)%
= 92%
Number of girls passed in exam
= 92% of q
= (92/100) x q
= 92q/100 -----(2)
From A, we have
p/q = 5/3
p = 5q/3
Total number of students passed in exam
= Number of boys passed in exam + Number of girls passed in exam
From equation (1) and (2),
Total number of students passed in exam = 84p/100 + 92q/100 ------(4)
Substitute p = 5q/3 in equation (4)
Total number of students passed in exam
= (84/100) x (5q/3) + 92q/100
= (28 x 5)q/100 + 92q/100
= (140 + 92)q/100
= 232q/100
Now, we will find total number of students.
Total number of students
= Number of boys + Number of girls
= p + q
= 5q/3 + q
[By Substituting p = 5q/3]
= 8q/3
Total pass percentage
= (Total number of students passed in exam/Total number of students) x 100
= [(232q/100)/(8q/3] x 100 %
= (232 x 3)/8
= 87%
