RAS question
In a pie chart of monthly expenditure, 'Food' has a central angle of 108°. If total expenditure is ₹25,000, the amount spent on food is:
Correct answer: (D) ₹7,500.
Food represents 108° out of the pie chart's full 360°, so the food expenditure is 30% of ₹25,000, which is ₹7,500.
Explanation
NCERT describes a pie chart as a circle graph in which the whole circle is divided into sectors, and the size of each sector is proportional to the information it represents. It also states that the total angle at the centre of a circle is 360°, so each sector's central angle is treated as a fraction of 360°. Here, Food has a central angle of 108°. Its share of the total expenditure is therefore 108/360 = 0.3, or 30%. Applying that share to the total monthly expenditure gives 0.3 × ₹25,000 = ₹7,500. Hence the amount spent on food is ₹7,500.
Why the other options are wrong
- (A) ₹9,000 would mean 36% of ₹25,000, but a 108° sector represents only 108/360 = 30% of the pie chart.
- (B) ₹8,000 is 32% of ₹25,000, which does not match the 30% share shown by a 108° sector.
- (C) ₹6,000 is 24% of ₹25,000, so it understates the share represented by the 108° central angle.
Concept
This tests data interpretation through pie charts: converting a sector's central angle into a fraction of the whole. It recurs in RAS reasoning because expenditure, marks, population-share and survey questions often reduce to proportional reading of 360° charts.