Data Interpretation

We need to calculate the number of students from Institute B in both Arts and Commerce streams and then add them.
Arts Students from Institute B: From the Arts pie chart, the percentage for Institute B is 8%. Total Arts students = 3800.
Number of Arts students in B = 8% of 3800 = .
Commerce Students from Institute B:
From the Commerce pie chart, the percentage for Institute B is 17%. Total Commerce students = 4200.
Number of Commerce students in B = 17% of 4200 = .
Total Students from Institute B: Total = Arts students + Commerce students = . The total number of students from Institute B is 1018.

Let's find the pattern by looking at the differences between consecutive terms. The sequence of differences is: -35, -40, -45, -55, -50, -60. There is a clear arithmetic progression in the differences: -35, -40, -45... The next difference should be -50.
Let's see where the pattern breaks.
-90 + (-50) = -140. The series has -145. This seems to be the error. Let's check if the rest of the series follows from -140.
The next difference should be -55.
-140 + (-55) = -195. (Matches) The next difference should be -60.
-195 + (-60) = -255. (Matches) The pattern holds if the term -145 is replaced by -140. Therefore, -145 is the wrong number.

We need to find the number of students in Institute E for both streams and then find their ratio.
Arts Students from Institute E:
From the Arts pie chart, the percentage for Institute E is 14%. Total Arts students = 3800.
Number of Arts students in E = 14% of 3800 = .
Commerce Students from Institute E:
From the Commerce pie chart, the percentage for Institute E is 18%. Total Commerce students = 4200.
Number of Commerce students in E = 18% of 4200 = .
Ratio: Ratio (Arts : Commerce) = 532 : 756. Now we simplify the ratio by finding the greatest common divisor. Both numbers are divisible by 4.
The ratio is 133 : 189. Both numbers are divisible by 7.
The simplified ratio is 19 : 27.