Following bar graph shows the percentage break-up of number of students preparing for bank exams in institutes X, Y and Z.

• In Institute X, a% of the students are preparing for the CAT exams.
• In Institute Y, b% of the students are preparing for the CAT exams.
• In Institute Z, c% of the students are preparing for the CAT exams.
• The central angle corresponding to the percentage of students preparing for bank exams in Institute Y is 162°.(If we suppose this bar graph represents the pie chart with same distribution)
• The count of students preparing for for CAT exams in Institute X is 1/9th of those preparing for the same exams in Institute Y.
• The total number of students in Institute X studying for bank exams is 90 less than the number at Institute Z preparing for the same.
• The total number of student at Institute X is half that of Institute Z.
• Institute Y has a student count of 540; this is 60 less than the total number of students involved in bank exam preparations across Institutes X, Y, and Z.