Match List - I with List - II: On the basis of share of expenditure in given pie chart.
Choose the correct answer from the options given below:
Show Hint
Simple fractions are easy to remember:
\(1/9\) is exactly \(11.11\%\). Since the Saving angle of 40\(^{\circ}\) is exactly \(1/9\) of 360\(^{\circ}\), Saving must be \(11.11\%\). This quickly pairs C with I, eliminating several options!
• Step 1: Understanding the Question: This question involves converting degrees from a pie chart into percentage values. We need to compute the percentage of expenditure for the categories of Rent, Transport, Saving, and Food, and match them with the options in List-II.
• Step 2: Key Formula or Approach:
The total angle at the center of a pie chart is 360\(^{\circ}\).
To convert any sector angle \(\theta\) (in degrees) to a percentage \(P\):
\[ P = \left(\frac{\theta}{360}\right) \times 100\% \]
• Step 3: Detailed Explanation:
Let us calculate the percentages for each category:
- A. Percentage of Expenditure on Rent:
Rent sector angle = 60\(^{\circ}\).
\[ \text{Percentage} = \left(\frac{60}{360}\right) \times 100\% = \frac{1}{6} \times 100\% \approx 16.67\% \]
This matches with III.
- B. Percentage of Expenditure on Transport:
Transport sector angle = 50\(^{\circ}\).
\[ \text{Percentage} = \left(\frac{50}{360}\right) \times 100\% = \frac{5}{36} \times 100\% \approx 13.89\% \]
This matches with II.
- C. Percentage of Expenditure on Saving:
Saving sector angle = 40\(^{\circ}\).
\[ \text{Percentage} = \left(\frac{40}{360}\right) \times 100\% = \frac{1}{9} \times 100\% \approx 11.11\% \]
This matches with I.
- D. Percentage of Expenditure on Food:
Food sector angle = 65\(^{\circ}\).
\[ \text{Percentage} = \left(\frac{65}{360}\right) \times 100\% = \frac{65}{3.6} \approx 18.06\% \]
This matches with IV.
Summarizing the matching:
- A matches with III
- B matches with II
- C matches with I
- D matches with IV
Therefore, the matching order is A-III, B-II, C-I, D-IV.
• Step 4: Final Answer: The correct matched list is (D).
