1.  Which section has the minimum failure rate in half yearly examination?
A. A section
B. B section
C. C section
D. D section
E. Cannot be determined

Answer: Option D

Explanation:

Total number of failures in half-yearly exams in a section

= [ (Number of students failed in both exams)

        + (Number of students failed in half-yearly but passed in Annual exams)

   ] in that section

Therefore Failure rate in half-yearly exams in Section A

= [ No of students of Sec A
failed in half-yearly		 x 100 ] %
Total no of students in Sec A

= [ (28 + 14) x 100 ] %
(28 + 14 + 6 + 64)

= [ 42 x 100 ] %
112

= 37.5%.

Similarly, failure rate in half-yearly exams in:

Section B

[ (23 + 12) x 100 ] % = [ 35 x 100 ] % 
(23 + 12 + 17 + 55) 107

= 32.71%.

Section C

[ (17 + 8) x 100 ] % = [ 25 x 100 ] % 
(17 + 8 + 9 + 46) 80

= 31.25%.

Section D

[ (27 + 13) x 100 ] % = [ 40 x 100 ] % 
(27 + 13 + 15 + 76) 131

= 30.53%.

Clearly, the failure rate is minimum for Section D.