3c. Problems based on Pie Charts

 3c. Problems based on Pie Charts

3. Problems Based on Pie Charts

Pie charts show data as proportions of a whole, often in percentages. Below are the 10 problems with full solutions.

Problem 1

Problem Statement:
A pie chart shows the distribution of a company’s budget ($10,000) across four categories:

  • Salaries: 40%
  • Rent: 30%
  • Supplies: 20%
  • Miscellaneous: 10%
    Question: How much is spent on Salaries, and what is the combined expenditure on Rent and Supplies?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows percentages of a $10,000 budget.
    • We need: (1) Amount for Salaries, (2) Combined amount for Rent and Supplies.
  • Calculate Salaries:
    • Salaries = 40% of $10,000
    • Salaries = (40 / 100) × 10,000 = 4000.
  • Calculate Rent and Supplies:
    • Rent = 30% of $10,000
    • Rent = (30 / 100) × 10,000 = 3000.
    • Supplies = 20% of $10,000
    • Supplies = (20 / 100) × 10,000 = 2000.
    • Combined = Rent + Supplies = 3000 + 2000 = 5000.
  • Verify:
    • Total budget: 4000 + 3000 + 2000 + (10% × 10,000) = 4000 + 3000 + 2000 + 1000 = 10,000.
    • Combined: 3000 + 2000 = 5000.
  • Present the Answer:
    • Salaries: $4000.
    • Combined Rent and Supplies: $5000.

Problem 2

Problem Statement:
Pie chart: Time spent (24 hours): Sleep: 33.33%, Work: 33.33%, Leisure: 33.33%.
Question: How many hours are spent on Work?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows time allocation in a 24-hour day.
    • We need the hours spent on Work.
  • Extract Relevant Data:
    • Work = 33.33% of 24 hours.
  • Calculate Hours:
    • Hours = (33.33 / 100) × 24
    • 33.33% ≈ 1/3, so (1/3) × 24 = 8.
    • Exact: 0.3333 × 24 = 7.9992 ≈ 8 (since 33.33% is approximate).
  • Verify:
    • Calculation: (33.33 ÷ 100) × 24 ≈ 8.
    • Total: 8 + 8 + 8 ≈ 24 hours.
  • Present the Answer:
    • Hours spent on Work: 8 hours.

Problem 3

Problem Statement:
Pie chart: Sales ($100,000): Product A: 50%, Product B: 30%, Product C: 20%.
Question: What is the sales value of Product B?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows sales distribution for a total of $100,000.
    • We need the sales value for Product B.
  • Extract Relevant Data:
    • Product B = 30% of $100,000.
  • Calculate Sales Value:
    • Sales = (30 / 100) × 100,000 = 30,000.
  • Verify:
    • Total: 50% + 30% + 20% = 100%.
    • Calculation: 0.3 × 100,000 = 30,000.
  • Present the Answer:
    • Sales value of Product B: $30,000.

Problem 4

Problem Statement:
Pie chart: Students’ grades: A: 25%, B: 40%, C: 20%, D: 15% (Total 200 students).
Question: How many students got a B?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows grade distribution for 200 students.
    • We need the number of students with a B.
  • Extract Relevant Data:
    • Grade B = 40% of 200 students.
  • Calculate Number of Students:
    • Students = (40 / 100) × 200 = 80.
  • Verify:
    • Total: 25% + 40% + 20% + 15% = 100%.
    • Calculation: 0.4 × 200 = 80.
  • Present the Answer:
    • Number of students with a B: 80.

Problem 5

Problem Statement:
Pie chart: Budget ($5000): Food: 20%, Rent: 50%, Transport: 15%, Savings: 15%.
Question: What is the combined expenditure on Food and Transport?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows budget distribution for $5000.
    • We need the combined expenditure on Food and Transport.
  • Extract Relevant Data:
    • Food = 20% of $5000.
    • Transport = 15% of $5000.
  • Calculate Expenditures:
    • Food = (20 / 100) × 5000 = 1000.
    • Transport = (15 / 100) × 5000 = 750.
    • Combined = Food + Transport = 1000 + 750 = 1750.
  • Verify:
    • Total: 20% + 50% + 15% + 15% = 100%.
    • Combined: 1000 + 750 = 1750.
  • Present the Answer:
    • Combined expenditure on Food and Transport: $1750.

Problem 6

Problem Statement:
Pie chart: Market share: Company A: 40%, Company B: 35%, Company C: 25%.
Question: If the total market is $1,000,000, what is Company C’s share?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows market share for a total of $1,000,000.
    • We need Company C’s share.
  • Extract Relevant Data:
    • Company C = 25% of $1,000,000.
  • Calculate Share:
    • Share = (25 / 100) × 1,000,000 = 250,000.
  • Verify:
    • Total: 40% + 35% + 25% = 100%.
    • Calculation: 0.25 × 1,000,000 = 250,000.
  • Present the Answer:
    • Company C’s share: $250,000.

Problem 7

Problem Statement:
Pie chart: Energy sources (100 units): Solar: 30%, Wind: 20%, Coal: 40%, Other: 10%.
Question: How many units come from Wind?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows energy sources for 100 units.
    • We need the units from Wind.
  • Extract Relevant Data:
    • Wind = 20% of 100 units.
  • Calculate Units:
    • Units = (20 / 100) × 100 = 20.
  • Verify:
    • Total: 30% + 20% + 40% + 10% = 100%.
    • Calculation: 0.2 × 100 = 20.
  • Present the Answer:
    • Units from Wind: 20 units.

Problem 8

Problem Statement:
Pie chart: Expenses ($2000): Rent: 45%, Utilities: 25%, Food: 20%, Misc: 10%.
Question: What is the difference between Rent and Food expenses?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows expense distribution for $2000.
    • We need the difference between Rent and Food expenses.
  • Extract Relevant Data:
    • Rent = 45% of $2000.
    • Food = 20% of $2000.
  • Calculate Expenses:
    • Rent = (45 / 100) × 2000 = 900.
    • Food = (20 / 100) × 2000 = 400.
    • Difference = Rent – Food = 900 – 400 = 500.
  • Verify:
    • Total: 45% + 25% + 20% + 10% = 100%.
    • Difference: 900 – 400 = 500.
  • Present the Answer:
    • Difference between Rent and Food: $500.

Problem 9

Problem Statement:
Pie chart: Votes (1000): Party A: 50%, Party B: 30%, Party C: 20%.
Question: How many more votes did Party A get than Party B?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows vote distribution for 1000 votes.
    • We need the difference in votes between Party A and Party B.
  • Extract Relevant Data:
    • Party A = 50% of 1000.
    • Party B = 30% of 1000.
  • Calculate Votes:
    • Party A = (50 / 100) × 1000 = 500.
    • Party B = (30 / 100) × 1000 = 300.
    • Difference = Party A – Party B = 500 – 300 = 200.
  • Verify:
    • Total: 50% + 30% + 20% = 100%.
    • Difference: 500 – 300 = 200.
  • Present the Answer:
    • Party A got 200 more votes than Party B.

Problem 10

Problem Statement:
Pie chart: Time allocation (60 minutes): Task A: 40%, Task B: 30%, Task C: 20%, Task D: 10%.
Question: How much time is spent on Task C?

Step-by-Step Solution:

  • Understand the Data:
    • The pie chart shows time allocation for 60 minutes.
    • We need the time spent on Task C.
  • Extract Relevant Data:
    • Task C = 20% of 60 minutes.
  • Calculate Time:
    • Time = (20 / 100) × 60 = 12.
  • Verify:
    • Total: 40% + 30% + 20% + 10% = 100%.
    • Calculation: 0.2 × 60 = 12.
  • Present the Answer:
    • Time spent on Task C: 12 minutes.

 

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