📝 Mock Test: Proportional Reasoning Practice | Ganita Prakash | Grade 8

9to9iMall November 05, 2025

Proportional Reasoning-1: Mock Test

Mock Test: Proportional Reasoning Practice | Ganita Prakash

Instructions: Read each problem carefully. Use the principles of ratios and proportions to find the solution. Remember to check your units and simplify ratios to their simplest form where required.

Figure It Out!

1. The Trail Mix Recipe
A recipe for a high-energy trail mix requires mixing cashews and dried apricots in the ratio of 5 : 3. If you want to make a large batch weighing 800 grams, how many grams of cashews and apricots will you need?

2. The Business Partnership
Two friends, Alisha and Ben, start a small online business. Alisha invests $9,000 and Ben invests $6,000. They agree to share their first month's profit of $2,500 in the same ratio as their investment. How much profit does each person receive?

3. The Marathon Runner
A marathon runner can run 8 kilometres in 40 minutes. If she maintains the same pace, how far will she run in 1.5 hours?

4. The Smoothie Surprise
A recipe for a berry smoothie uses raspberries and blueberries in a ratio of 2 : 5. You make a 700 mL smoothie following this recipe. To make it more "raspberry-ish," you decide to add an extra 100 mL of pure raspberry puree. What is the new ratio of raspberries to blueberries in your smoothie?

5. The Video Editing Grind
A YouTuber finds that it takes approximately 3 hours to edit a 10-minute video. For a special episode, they have filmed 45 minutes of content that needs to be edited down to a final video. Based on their usual rate, how many hours should they budget for editing?

6. The Painting Project (Advanced Question!)
It takes 4 people 6 hours to paint a large wall. If the project needs to be finished faster and 2 more people join the team (for a total of 6 people), how long will it take them to paint the same wall, assuming everyone works at the same rate? (Hint: Think carefully! Is this a standard proportion?)

Answer Key & Solutions

1. The Trail Mix Recipe

  • Total parts: 5 (cashews) + 3 (apricots) = 8 parts.
  • Value of one part: 800 g / 8 parts = 100 g per part.
  • Cashews (5 parts): 5 × 100 g = 500 g.
  • Apricots (3 parts): 3 × 100 g = 300 g.
  • Answer: You will need 500 g of cashews and 300 g of apricots.

2. The Business Partnership

  • Investment Ratio: Alisha : Ben = 9000 : 6000.
  • Simplest Form: Divide both by 3000 to get the ratio 3 : 2.
  • Total parts: 3 + 2 = 5 parts.
  • Value of one part: $2,500 / 5 parts = $500 per part.
  • Alisha's Profit (3 parts): 3 × $500 = $1,500.
  • Ben's Profit (2 parts): 2 × $500 = $1,000.
  • Answer: Alisha receives $1,500 and Ben receives $1,000.

3. The Marathon Runner

  • Unit Conversion: The pace is in minutes, but the new time is in hours. We must use the same unit. 1.5 hours = 1.5 × 60 = 90 minutes.
  • Set up the proportion: (Distance : Time) :: (New Distance : New Time)
    8 km : 40 min :: ? km : 90 min
  • Method 1 (Find the factor): The time has changed by a factor of 90 / 40 = 2.25. So, the distance will also change by this factor. 8 km × 2.25 = 18 km.
  • Method 2 (Unit Rate): Pace = 8 km / 40 min = 0.2 km per minute. Distance in 90 minutes = 0.2 km/min × 90 min = 18 km.
  • Answer: She will run 18 km.

4. The Smoothie Surprise

  • Part A (Initial Amounts):
    • Total parts: 2 (raspberries) + 5 (blueberries) = 7 parts.
    • Volume of one part: 700 mL / 7 = 100 mL.
    • Initial Raspberries: 2 × 100 mL = 200 mL.
    • Initial Blueberries: 5 × 100 mL = 500 mL.
  • Part B (New Amounts):
    • New Raspberries: 200 mL + 100 mL (added) = 300 mL.
    • Blueberries: 500 mL (unchanged).
  • New Ratio: Raspberries : Blueberries = 300 : 500.
  • Simplest Form: Divide both by 100. The new ratio is 3 : 5.

5. The Video Editing Grind

  • Set up the proportion: (Editing Time : Video Length) :: (New Editing Time : New Video Length)
    3 hours : 10 min :: ? hours : 45 min
  • Find the factor: The video length is 4.5 times longer (45 min / 10 min = 4.5).
  • Calculate New Editing Time: The editing time will also be 4.5 times longer.
    3 hours × 4.5 = 13.5 hours.
  • Answer: They should budget 13.5 hours for editing.

6. The Painting Project (Advanced Question!)

  • Identify the relationship: This is an inverse proportion. More people means less time.
  • Calculate total "person-hours": The total work required is 4 people × 6 hours = 24 person-hours.
  • Calculate new time: With 6 people, the time taken is the total work divided by the number of people.
    Time = 24 person-hours / 6 people = 4 hours.
  • Answer: It will take the team of 6 people 4 hours to paint the wall.
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