In a family budget, 30% is spent on rent, 25% on food, 15% on education, 20% on savings, and 10% on miscellaneous. The central angle for 'Education' in a pie chart is:

Explanation

In a pie chart, the full circle represents 100% of the data and measures 360 degrees. NCERT's treatment of percentages frames percent as per hundred, so a 15% share means 15 parts out of the total 100 parts. The central angle for any sector is therefore its percentage share of 360 degrees. For Education, the calculation is (15/100) x 360 degrees = 54 degrees. This matches the idea that each component's angle is proportional to its percentage share: Rent at 30% would occupy a larger sector, while Education at 15% occupies a smaller sector equal to 54 degrees.

Why the other options are wrong

• (B) 45 degrees would correspond to 12.5% of a 360-degree circle, not the given 15% share for Education.
• (C) 60 degrees would represent 16.67% of the circle, which is more than the stated Education share of 15%.
• (D) 72 degrees would correspond to 20% of the circle, which is the Savings share in the question, not Education.

Concept

This tests percentage-to-angle conversion in data interpretation, a recurring RAS reasoning topic because budget, survey, and distribution questions often require translating shares into pie-chart sectors.

Source

• NCERT Class VII Mathematics Exemplar Problems, Unit 7: Comparing Quantities

Related questions

• 4 : 16 :: 6 : ?
• 8 : 27 :: 64 : ?
• A and B independently try to solve a problem. The probability that A solves it is 1/3 and that B solves it is 2/5. The probability that the problem is solved is:
• A bag has 5 red and 3 blue balls. Two balls are drawn without replacement. The probability that both are red is:
• A bar diagram shows the number of students in 5 sections: A=45, B=50, C=35, D=40, E=30. The ratio of students in the largest section to the smallest section is:
• A clock seen in a mirror shows 8:20. What is the actual time?