30b. Problems based on Graphs

2. Problems Based on Graphs

Graphs (e.g., bar graphs, line graphs) visually represent data, often showing trends or comparisons. Below are the 10 problems with full solutions.

Problem 1

Problem Statement:
A bar graph shows the revenue (in $1000) of a company from three products (X, Y, Z) over two years (2023, 2024).

  • 2023: X = 50, Y = 40, Z = 30.
  • 2024: X = 60, Y = 45, Z = 35.
    Question: What is the percentage increase in revenue for Product X from 2023 to 2024?

Step-by-Step Solution:

  • Understand the Data:
    • The bar graph shows revenue in $1000 for three products over two years.
    • We need the percentage increase for Product X from 2023 to 2024.
  • Extract Relevant Data:
    • Product X revenue: 2023 = 50 ($50,000), 2024 = 60 ($60,000).
  • Calculate Increase:
    • Increase = 2024 revenue – 2023 revenue
    • Increase = 60 – 50 = 10.
  • Calculate Percentage Increase:
    • Percentage increase = (Increase / 2023 revenue) × 100
    • Percentage increase = (10 / 50) × 100 = 20%.
  • Verify:
    • Increase: 60 – 50 = 10.
    • Percentage: (10 ÷ 50) × 100 = 20.
  • Present the Answer:
    • Percentage increase for Product X: 20%.

Problem 2

Problem Statement:
Line graph: Monthly sales (in units) of a product (Jan: 100, Feb: 120, Mar: 150).
Question: What is the total sales over three months?

Step-by-Step Solution:

  • Understand the Data:
    • The line graph shows monthly sales for a product over three months.
    • We need the total sales.
  • Extract Relevant Data:
    • Sales: Jan = 100, Feb = 120, Mar = 150.
  • Calculate Total:
    • Total = Jan + Feb + Mar
    • Total = 100 + 120 + 150 = 370.
  • Verify:
    • Sum: 100 + 120 = 220, 220 + 150 = 370.
  • Present the Answer:
    • Total sales: 370 units.

Problem 3

Problem Statement:
Bar graph: Scores of four students (A: 80, B: 85, C: 90, D: 75).
Question: What is the average score?

Step-by-Step Solution:

  • Understand the Data:
    • The bar graph shows scores for four students.
    • We need the average score.
  • Extract Relevant Data:
    • Scores: A = 80, B =

85, C = 90, D = 75.

  • Calculate Average:
    • Average = (A + B + C + D) / Number of students
    • Sum = 80 + 85 + 90 + 75 = 330.
    • Average = 330 / 4 = 82.5.
  • Verify:
    • Sum: 80 + 85 = 165, 165 + 90 = 255, 255 + 75 = 330.
    • Average: 330 ÷ 4 = 82.5.
  • Present the Answer:
    • Average score: 82.5.

Problem 4

Problem Statement:
Line graph: Temperature (°C) over a week (Mon: 20, Tue: 22, Wed: 21, Thu: 23, Fri: 24).
Question: What is the difference between the highest and lowest temperatures?

Step-by-Step Solution:

  • Understand the Data:
    • The line graph shows daily temperatures over five days.
    • We need the difference between the highest and lowest temperatures.
  • Extract Relevant Data:
    • Temperatures: Mon = 20, Tue = 22, Wed = 21, Thu = 23, Fri = 24.
    • Highest = 24 (Fri), Lowest = 20 (Mon).
  • Calculate Difference:
    • Difference = Highest – Lowest
    • Difference = 24 – 20 = 4.
  • Verify:
    • Highest = 24, Lowest = 20.
    • Difference: 24 – 20 = 4.
  • Present the Answer:
    • Difference between highest and lowest temperatures: 4°C.

Problem 5

Problem Statement:
Bar graph: Production (in tons) of two factories (F1: 500, F2: 600).
Question: What is the percentage of F1’s production relative to the total?

Step-by-Step Solution:

  • Understand the Data:
    • The bar graph shows production for two factories.
    • We need F1’s production as a percentage of the total.
  • Extract Relevant Data:
    • Production: F1 = 500, F2 = 600.
  • Calculate Total Production:
    • Total = F1 + F2
    • Total = 500 + 600 = 1100.
  • Calculate Percentage:
    • Percentage = (F1 / Total) × 100
    • Percentage = (500 / 1100) × 100 ≈ 45.4545%.
    • Rounded to two decimal places: 45.45%.
  • Verify:
    • Total: 500 + 600 = 1100.
    • Percentage: (500 ÷ 1100) × 100 ≈ 45.45.
  • Present the Answer:
    • Percentage of F1’s production: 45.45%.

Problem 6

Problem Statement:
Line graph: Stock prices ($): Day 1: 50, Day 2: 52, Day 3: 55, Day 4: 53.
Question: What is the average stock price?

Step-by-Step Solution:

  • Understand the Data:
    • The line graph shows stock prices over four days.
    • We need the average stock price.
  • Extract Relevant Data:
    • Prices: Day 1 = 50, Day 2 = 52, Day 3 = 55, Day 4 = 53.
  • Calculate Average:
    • Average = (Day 1 + Day 2 + Day 3 + Day 4) / Number of days
    • Sum = 50 + 52 + 55 + 53 = 210.
    • Average = 210 / 4 = 52.5.
  • Verify:
    • Sum: 50 + 52 = 102, 102 + 55 = 157, 157 + 53 = 210.
    • Average: 210 ÷ 4 = 52.5.
  • Present the Answer:
    • Average stock price: $52.5.

Problem 7

Problem Statement:
Bar graph: Visitors to a museum (Jan: 2000, Feb: 2500, Mar: 3000).
Question: What is the percentage increase from Jan to Mar?

Step-by-Step Solution:

  • Understand the Data:
    • The bar graph shows monthly visitors to a museum.
    • We need the percentage increase from Jan to Mar.
  • Extract Relevant Data:
    • Visitors: Jan = 2000, Mar = 3000.
  • Calculate Increase:
    • Increase = Mar – Jan
    • Increase = 3000 – 2000 = 1000.
  • Calculate Percentage Increase:
    • Percentage increase = (Increase / Jan) × 100
    • Percentage increase = (1000 / 2000) × 100 = 50%.
  • Verify:
    • Increase: 3000 – 2000 = 1000.
    • Percentage: (1000 ÷ 2000) × 100 = 50.
  • Present the Answer:
    • Percentage increase: 50%.

Problem 8

Problem Statement:
Line graph: Rainfall (mm) over five days (10, 15, 20, 25, 30).
Question: What is the total rainfall?

Step-by-Step Solution:

  • Understand the Data:
    • The line graph shows daily rainfall over five days.
    • We need the total rainfall.
  • Extract Relevant Data:
    • Rainfall: Day 1 = 10, Day 2 = 15, Day 3 = 20, Day 4 = 25, Day 5 = 30.
  • Calculate Total:
    • Total = Day 1 + Day 2 + Day 3 + Day 4 + Day 5
    • Total = 10 + 15 + 20 + 25 + 30 = 100.
  • Verify:
    • Sum: 10 + 15 = 25, 25 + 20 = 45, 45 + 25 = 70, 70 + 30 = 100.
  • Present the Answer:
    • Total rainfall: 100 mm.

Problem 9

Problem Statement:
Bar graph: Expenses ($): Food: 400, Rent: 800, Utilities: 200.
Question: What fraction of total expenses is Rent?

Step-by-Step Solution:

  • Understand the Data:
    • The bar graph shows expenses in three categories.
    • We need the fraction of total expenses that is Rent.
  • Extract Relevant Data:
    • Expenses: Food = 400, Rent = 800, Utilities = 200.
  • Calculate Total Expenses:
    • Total = Food + Rent + Utilities
    • Total = 400 + 800 + 200 = 1400.
  • Calculate Fraction:
    • Fraction = Rent / Total
    • Fraction = 800 / 1400 = 8/14 = 4/7 (simplified).
  • Verify:
    • Total: 400 + 800 = 1200, 1200 + 200 = 1400.
    • Fraction: 800 ÷ 1400 = 8/14, simplifies to 4/7.
  • Present the Answer:
    • Fraction of total expenses for Rent: 4/7.

Problem 10

Problem Statement:
Line graph: Distance traveled (km) by a car (Hour 1: 50, Hour 2: 100, Hour 3: 150).
Question: What is the average speed?

Step-by-Step Solution:

  • Understand the Data:
    • The line graph shows cumulative distance traveled over three hours.
    • We need the average speed (distance/time).
  • Extract Relevant Data:
    • Total distance after 3 hours = 150 km.
    • Total time = 3 hours.
  • Calculate Average Speed:
    • Average speed = Total distance / Total time
    • Average speed = 150 / 3 = 50 km/h.
  • Verify:
    • Distance = 150 km, Time = 3 hours.
    • Speed: 150 ÷ 3 = 50.
  • Present the Answer:
    • Average speed: 50 km/h.

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