RAS question
In a family budget: Rent 30%, Food 25%, Education 15%, Savings 20%, Misc 10%. The central angle for 'Education' in a pie chart is:
Correct answer: (D) 54°.
In the family-budget pie chart, Education occupies 15% of the whole, so its central angle is 54 degrees.
Explanation
NCERT explains a pie chart as a circle graph in which the whole is split into sectors, with each sector showing its share of the total. Since a full circle has 360 degrees at the centre, the central angle for any category is its percentage share divided by 100 and then multiplied by 360. Education is given as 15% of the family budget, so its sector angle is (15/100) x 360 = 54 degrees. This is why option D is correct: the calculation converts the percentage share of Education into the matching angle in the circle.
Why the other options are wrong
- (A) 72 degrees would represent 20% of the whole circle, which matches the Savings share, not Education.
- (B) 45 degrees represents 12.5% of a full 360-degree circle, whereas Education is 15%.
- (C) 60 degrees represents one-sixth of the circle, about 16.67%, so it is larger than the 15% Education share.
Concept
This tests percentage-to-angle conversion in pie charts under data interpretation. It recurs in RAS reasoning because budget, population, and expenditure charts often require translating a share of the whole into a central angle.