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Difficulty: HardBasic Tools of Economic Analysis

In a state government budget presentation, a total expenditure of ₦720 million₦720\text{ million} is represented on a pie chart. The sectorial allocation for Education is represented by an angle of 120∘120^\circ and Infrastructure by 90∘90^\circ. If the remaining budget is allocated between Health and Agriculture in the ratio 3:23:2 respectively, what is the total monetary amount allocated to Health?

  1. A
    ₦120 million₦120\text{ million}
  2. ₦180 million₦180\text{ million}Answer
  3. C
    ₦300 million₦300\text{ million}
  4. D
    ₦240 million₦240\text{ million}

Answer

The total monetary amount allocated to Health is ₦180 million₦180\text{ million}.
The remaining sectors (Health and Agriculture) cover an angle of 360∘−(120∘+90∘)=150∘360^\circ - (120^\circ + 90^\circ) = 150^\circ. Distributing 150∘150^\circ in the ratio 3:23:2 assigns Health an angle of 35×150∘=90∘\frac{3}{5} \times 150^\circ = 90^\circ. Converting this angle into monetary terms relative to the total budget of ₦720 million₦720\text{ million} gives 90∘360∘×₦720 million=₦180 million\frac{90^\circ}{360^\circ} \times ₦720\text{ million} = ₦180\text{ million}.

Step-by-Step Solution

1
Calculate the sum of the known sectorial angles on the pie chart.
Known angles = 120∘+90∘=210∘120^\circ + 90^\circ = 210^\circ.
Education and Infrastructure account for 210∘210^\circ of the total 360∘360^\circ pie chart.
2
Determine the remaining angle for Health and Agriculture combined.
Remaining angle = 360∘−210∘=150∘360^\circ - 210^\circ = 150^\circ.
A full pie chart represents 360∘360^\circ.
3
Calculate the specific angle allocated to Health using the ratio 3:23:2.
Health angle = 33+2×150∘=35×150∘=90∘\frac{3}{3 + 2} \times 150^\circ = \frac{3}{5} \times 150^\circ = 90^\circ.
Health gets 3 parts out of a total of 5 ratio parts.
4
Convert the Health sector angle to monetary value.
Health expenditure = 90∘360∘×₦720 million=₦180 million\frac{90^\circ}{360^\circ} \times ₦720\text{ million} = ₦180\text{ million}.
The monetary value is proportional to the ratio of the sector angle to 360∘360^\circ multiplied by the total budget.

Key Concept

Pie Chart Angle Computation and Fractional Data Interpretation
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Topics

Basic Tools of Economic Analysis

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