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

 Failure rate in half-yearly exams in Section A

= \( (\frac { Number of students of setion A failed in half- yearly } { Total numbers of students in setion A} ) \)

= [ \(\frac { (28+14) } {(28+14+6+64) } \) X 100] %

=[ \(\frac { 42} { 112 } \) X 100 ]%

= 37.5%

Similarly, failure rate in half-yearly exams in:

section B [  \(\frac { (23+12) } { (23+12+17+55) } \)x 100]% = [ \(\frac { 35 } { 107 }\) x 100 ] % = 32.71%

section C [ \( \frac { (17+8)} { (17+8+9+46) }\) x 100 ]% = [ \(\frac { 25 } { 80 }\) x 100 ]%= 31.25% 

section D [ \(\frac { (27+13) } { (27+13+15+76)} \) x 100 ]% = [ \(\frac { 40 } { 131 }\) x 100] % =30.53%

Clearly, the failure rate is minimum for Section D.