Correct Answer: 56.25%

Solution : Total Number of Students passed = 900
The number of students who passed the examination from institute C = 30$^\circ$
= $(\frac{30}{100}\times 900)$
= 270
Total Number of Students appeared = 1200
The number of students who appeared from institutes D = 105$^\circ$
= $(\frac{105}{360}\times 1200)$
= 350
The number of students who appeared from institutes E = 39$^\circ$
= $(\frac{39}{360}\times 1200)$
= 130
The total number of students who appeared from institutes D and E = (350 + 130) = 480
Now,
The number of students who passed the examination from institute C to the total number of students who appeared from institutes D and E
= $(\frac{270}{480}\times 100)$
= 56.25%
$\therefore$ The required percentage is 56.25%
Hence, the correct answer is 56.25%.