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The number of students taking admission in First Year of a Degree Course at a college in areas of Social Sciences in 2012 was as follows: Economics (S1) - 96, Psychology (S2) - 84, History (S3) - 160. Political Science (S4) - 120. Sociology (S5) - 125. The break-up of students in different subjects has been presented through the given pie chart. Study the pie chart and answer the question that follows. In 2013, 20% of the Sociology students, 25% of the Political Science students, and one-sixth of the Economics students shifted to another college, and the number of History students got increased by 10% due to students shifting from other colleges. Over and above this, 10% of the remaining Sociology students and one-seventh of the Psychology students got transferred to Economics. What will be the central angle (to the nearest degree) of the sector corresponding to History in the pie chart, representing the break-up in 2013? 

The number of students taking admission in First Year of a Degree Course at a college in areas of Social Sciences in 2012 was as follows: Economics (S1) - 96, Psychology (S2) - 84, History (S3) - 160. Political Science (S4) - 120. Sociology (S5) - 125. The break-up of students in different subjects has been presented through the given pie chart. Study the pie chart and answer the question that follows. In 2013, 20% of the Sociology students, 25% of the Political Science students, and one-sixth of the Economics students shifted to another college, and the number of History students got increased by 10% due to students shifting from other colleges. Over and above this, 10% of the remaining Sociology students and one-seventh of the Psychology students got transferred to Economics. What will be the central angle (to the nearest degree) of the sector corresponding to History in the pie chart, representing the break-up in 2013?  Correct Answer 120

Calculation: 

In 2012.

Economics - 96

Psychology - 84

History - 160

Political Science - 120

Sociology - 125

In 2013,

Sociology students = 125 × 0.8 = 100

Political science students = 120 × 0.75 = 90

Economics students = 96 × 5/6 = 80

History students = 160 × 1.1 = 176

Again,

the final number of student in Sociology = 100 × 0.9 = 90

the final number of student in Psychology = 84 × 6/7 = 72

the final number of student in Economics = 80 + 100 × 0.1 + 84 × 1/7 = 102

Total student in 2013 = 102 + 90 + 72 + 90 + 176 = 530

Central angle corresponding to History = (176/530) × 360 ≈ 120°

∴ The central angle (to the nearest degree) of the sector corresponding to History in the pie chart, representing the break-up in 2013.

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