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The results of half yearly and annual examinations are shown in the table given below:

Results
No. of students in section A
No. of students in section B
No. of students in section C
No. of students in section D
Students failed in both exams
28
23
17
27
Students failed in half yearly but passed in annual exam
14
12
8
13
Students passed in half yearly but failed in annual exam
6
17
9
15
Students passed in both exams
64
55
46
76

Which section has the minimum failure rate in half yearly?

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A section

B section

C section

D section

answer is D.

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Detailed Solution

Section A has a total of (28+14+6+64)=112 students.
Section B has a total of (23+12+17+55)=107 students.
Section C has a total of (17+8+9+46)=80 students.
Section D has a total of (27+13+15+76)=131 students.
Now, let us find the total no. of students who failed in the half yearly examination in each section.
Section A has a total of (28+14)=42 students failed in half yearly examinations.
Section B has a total of (23+12)=35 students failing in half yearly examinations.
Section C has a total of (17+8)=25 students failed in half yearly examinations.
Section D has a total of (27+13)=40 students failed in half yearly examinations.
Failure rate for section A =

\frac{42}{112} \times 100 = 37.5 %

Failure rate for section B =

\frac{35}{107} \times 100 = 32.7 %

Failure rate for section C =

\frac{25}{80} \times 100 = 31.25 %

Failure rate for section D =

\frac{40}{131} \times 100 = 30.5 %

Section D has a minimum failure rate in half yearly examinations.

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