Correct Answer: 5 : 4

Solution : From the pie chart, the percentage of students who passed Institute A is 22%.
So, the number of students who passed Institute A = 22% of 1200 = 264 students.
The ratio of boys to girls who passed from Institute A is 5 : 6.
So, the number of boys who passed from Institute A = $\frac{5}{11}$ × 264 = 120 boys
The percentage of students who passed Institute D is 20%.
So, the number of students who passed Institute D = 20% of 1200 = 240 students
Since 40% of these are boys, the number of boys who passed from Institute D = 40% of 240 = 96 boys
So, the ratio of the number of boys who passed from Institute A to that from Institute D
$=\frac{120}{96} = \frac{5}{4}$
Hence, the correct answer is 5 : 4.