RAS question
In a pie chart showing monthly expenditure, the central angle for 'Food' is 108°. If the total monthly expenditure is ₹25,000, the expenditure on food is:
Correct answer: (C) ₹7,500.
Food accounts for 108° out of the pie chart’s total 360°, so the food expenditure is 30% of ₹25,000, which is ₹7,500.
Explanation
NCERT explains that a pie chart, or circle graph, shows the relationship between a whole and its parts, with each sector’s size proportional to the information it represents. It also states that the total angle at the centre of a circle is 360°, so a sector’s central angle is a fraction of 360°. Here, Food is represented by 108°, so its share of total expenditure is 108/360 = 0.3. Applying that share to the total monthly expenditure gives 0.3 × ₹25,000 = ₹7,500. That matches option C.
Why the other options are wrong
- (A) ₹6,000 would represent 24% of ₹25,000, but the 108° sector represents 30% of the full 360° circle.
- (B) ₹8,000 is too high because it treats Food as 32% of the total, whereas 108/360 gives exactly 30%.
- (D) ₹9,000 would correspond to 36% of total expenditure, not to a 108° sector in a 360° pie chart.
Concept
This tests data interpretation through pie charts: converting a central angle into a part of the whole. It recurs in RAS because reasoning papers often ask candidates to translate chart proportions into actual values quickly and accurately.