Mock Test Chapter 7 Proportional Reasoning-1

9to9iMall November 05, 2025
Mock Test Chapter 7 Proportional Reasoning-1

📝 Mock Test: Proportional Reasoning Practice

📌 Instructions: This mock test is inspired by Chapter 7 - Proportional Reasoning. Try to solve each problem on your own first before checking the solutions. Good luck! 🎯

💵 Problem 1: Sharing Prize Money

Three friends Aarav, Priya, and Rohan won a prize of ₹7,200 in a competition. They decided to divide it in the ratio 3 : 4 : 5. How much money will each person receive?
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Step-by-Step Solution:

  1. Find the total parts: 3 + 4 + 5 = 12 total parts.
  2. Find the value of one part: ₹7,200 ÷ 12 = ₹600 per part.
  3. Calculate each share:
    • Aarav (3 parts): 3 × ₹600 = ₹1,800
    • Priya (4 parts): 4 × ₹600 = ₹2,400
    • Rohan (5 parts): 5 × ₹600 = ₹3,000
✅ Aarav gets ₹1,800, Priya gets ₹2,400, and Rohan gets ₹3,000.

🍹 Problem 2: Making Juice Concentrate

A juice concentrate contains mango pulp and water in the ratio 2 : 7. If you want to prepare 450 mL of this juice, how much mango pulp and water should you use? If you then add 100 mL more water to make it less concentrated, what will be the new ratio?
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Part A: Initial Mixture (450 mL)

  1. Total parts: 2 (mango) + 7 (water) = 9 total parts.
  2. Volume of one part: 450 mL ÷ 9 = 50 mL per part.
  3. Calculate amounts:
    • Mango pulp (2 parts): 2 × 50 mL = 100 mL
    • Water (7 parts): 7 × 50 mL = 350 mL

Part B: After Adding Water

  1. Mango pulp: Remains 100 mL.
  2. New water amount: 350 mL + 100 mL = 450 mL.
  3. New ratio: Mango : Water = 100 : 450.
  4. Simplify: Divide both by 50 → 2 : 9.
✅ Initially: 100 mL mango pulp and 350 mL water. New ratio: 2 : 9.

🏫 Problem 3: School Population Ratio

In a school, the ratio of boys to girls is 5 : 4. If there are 360 students in total, how many boys and how many girls are there? If 20 new girls join the school, what will be the new ratio of boys to girls?
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Part A: Current School Population

  1. Total parts: 5 (boys) + 4 (girls) = 9 total parts.
  2. Number per part: 360 ÷ 9 = 40 students per part.
  3. Calculate each group:
    • Boys (5 parts): 5 × 40 = 200 boys
    • Girls (4 parts): 4 × 40 = 160 girls

Part B: After 20 New Girls Join

  1. Boys: Remains 200.
  2. New girls count: 160 + 20 = 180 girls.
  3. New ratio: Boys : Girls = 200 : 180.
  4. Simplify: Divide both by 20 → 10 : 9.
✅ Currently: 200 boys and 160 girls. New ratio: 10 : 9.

🍪 Problem 4: Baking Cookies

A cookie recipe requires flour, sugar, and butter in the ratio 8 : 3 : 2. If you want to make cookies using 260 grams of this mixture, how much of each ingredient do you need?
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Step-by-Step Solution:

  1. Total parts: 8 (flour) + 3 (sugar) + 2 (butter) = 13 total parts.
  2. Weight of one part: 260 g ÷ 13 = 20 grams per part.
  3. Calculate each ingredient:
    • Flour (8 parts): 8 × 20 g = 160 g
    • Sugar (3 parts): 3 × 20 g = 60 g
    • Butter (2 parts): 2 × 20 g = 40 g
✅ You need 160 g flour, 60 g sugar, and 40 g butter.

🚗 Problem 5: Speed and Distance

A car travels 240 km in 4 hours. If it maintains the same speed, how far will it travel in 7 hours? How long will it take to cover 420 km?
👁️ Click to View Solution

Part A: Distance in 7 Hours

  1. Find the speed: Speed = Distance ÷ Time = 240 km ÷ 4 hours = 60 km/h.
  2. Calculate distance in 7 hours: Distance = Speed × Time = 60 km/h × 7 hours = 420 km.

Part B: Time to Cover 420 km

  1. Use the speed: Time = Distance ÷ Speed = 420 km ÷ 60 km/h = 7 hours.
✅ The car will travel 420 km in 7 hours. It takes 7 hours to cover 420 km.

🏗️ Problem 6: Construction Workers

If 8 workers can build a wall in 12 days, how many days will it take for 6 workers to build the same wall, assuming they all work at the same rate?
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Step-by-Step Solution:

  1. Find total work: Total work = 8 workers × 12 days = 96 worker-days.
  2. Calculate days for 6 workers: Days = Total work ÷ Number of workers = 96 ÷ 6 = 16 days.

💡 Concept: This is an example of inverse proportion. When the number of workers decreases, the time taken increases proportionally.

✅ It will take 6 workers 16 days to build the same wall.

🛒 Problem 7: Shopping for Fruits

The cost of 5 kg of apples is ₹400. What will be the cost of 8 kg of apples at the same rate? How many kilograms of apples can you buy for ₹640?
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Part A: Cost of 8 kg

  1. Find the rate: Rate = ₹400 ÷ 5 kg = ₹80 per kg.
  2. Calculate cost for 8 kg: Cost = ₹80 × 8 = ₹640.

Part B: Quantity for ₹640

  1. Use the rate: Quantity = ₹640 ÷ ₹80 per kg = 8 kg.
✅ 8 kg of apples will cost ₹640. You can buy 8 kg for ₹640.

🎨 Problem 8: Mixing Colors (Advanced)

A painter has two buckets. Bucket A contains red and white paint mixed in the ratio 2 : 3. Bucket B contains red and white paint mixed in the ratio 3 : 4. If the painter mixes the entire contents of both buckets together, and each bucket originally contained 5 liters, what will be the ratio of red to white paint in the final mixture?
👁️ Click to View Solution

Step-by-Step Solution:

Bucket A Analysis:

  1. Ratio: Red : White = 2 : 3, Total parts = 5.
  2. Volume per part: 5 liters ÷ 5 = 1 liter per part.
  3. Amounts in Bucket A:
    • Red: 2 × 1 = 2 liters
    • White: 3 × 1 = 3 liters

Bucket B Analysis:

  1. Ratio: Red : White = 3 : 4, Total parts = 7.
  2. Volume per part: 5 liters ÷ 7 ≈ 0.714 liters per part.
  3. Amounts in Bucket B:
    • Red: 3 × 0.714 ≈ 2.14 liters
    • White: 4 × 0.714 ≈ 2.86 liters

Final Mixture:

  1. Total Red: 2 + 2.14 = 4.14 liters (or exactly 30/7 liters).
  2. Total White: 3 + 2.86 = 5.86 liters (or exactly 41/7 liters).
  3. Ratio: Red : White = 30/7 : 41/7 = 30 : 41.
✅ The final ratio of red to white paint is 30 : 41.

🎯 Test Complete!

Great job working through these problems! Proportional reasoning is all about understanding relationships between quantities. The more you practice, the easier it becomes.

💪 Pro Tips:

  • Always identify the total parts first
  • Check if it's direct proportion (both increase) or inverse proportion (one increases, other decreases)
  • Simplify ratios to their lowest terms when possible
  • Don't forget to verify your answer makes sense in context!

Keep practicing and you'll master proportional reasoning! 🚀

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