Question : Study the given pie charts and answer the question that follows.
If the ratio of the number of boys to that of the girls who passed from Institute A is 5 : 6, and 40% of the students who passed from Institute D are boys, then the ratio of the number of boys who passed from Institute A to that of boys who passed from institute D is:
Option 1: 25 : 24
Option 2: 4 : 3
Option 3: 5 : 4
Option 4: 3 : 2
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.
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