Question

The ratio of boys and girls in a class is 5:3. If 16% of boys and 8% of girls failed in an examination, then find the percentage of passed students.

• A. 79%
• B. 87%
• C. 110%
• D. 120%

Answer 1

The correct option is B 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) $\times$p
= 16p/100

Percentage of girls failed in exam is 8%.
Number of girls failed in exam
= 8% of q
= (8/100) $\times$q
= 8q/100

Percentage of boys passed in exam
= (100 - 16)%
= 84%

Number of boys passed in exam
= 84% of p
= (84/100) $\times$ p
= 84p/100 -----(1)

Percentage of girls passed in exam
= (100 - 8)%
= 92%

Number of girls passed in exam
= 92% of q
= (92/100) $\times$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) $\times$(5q/3) + 92q/100
= (28 $\times$ 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) $\times$ 100
= [(232q/100)/(8q/3] $\times$ 100 %
= (232 $\times$ 3)/8
= 87%