Proportional Reasoning II is an important chapter in CBSE Board Class 8 Maths Ganita Prakash Part 2 that helps students understand the relationship between different quantities. This chapter explains how ratios, proportions, and comparison methods are used to solve mathematical problems in daily life.
Through Class 8 Maths Chapter 3 Proportional Reasoning 2 MCQs with Answers, students can revise important concepts like equivalent ratios, direct proportion, inverse proportion, unit method, and practical applications. Practicing these MCQs helps students improve their calculation skills and understand how quantities change in different situations.
Students preparing for school exams can also explore more Class 8 MCQs for regular revision. Solving chapter-wise Class 8 Maths MCQs helps build confidence, improve accuracy, and strengthen important Maths concepts step by step.
Chapter 3 Proportional Reasoning 2 Class 8 Maths MCQs
Practice these MCQs to revise important concepts like ratio, proportion, direct proportion, inverse proportion, unit method, scale factor, and real-life applications of Proportional Reasoning 2.
Q. Which of the following correctly explains a ratio?
A. A method to find only the total value
B. A comparison between two or more quantities
C. A way to measure only angles
D. A method used only for shapes
Answer: B. A comparison between two or more quantities
Explanation: A ratio is used to compare two or more quantities and understand the relationship between them.
Q. If the ratio of pencils to erasers is 4 : 7, what does the number 4 represent?
A. Number of eraser parts
B. Total number of items
C. Number of pencil parts
D. Difference between pencils and erasers
Answer: C. Number of pencil parts
Explanation: In the ratio 4 : 7, the first value represents pencils and the second value represents erasers.
Q. What is the term used when two ratios are equal?
A. Average
B. Fraction
C. Percentage
D. Proportion
Answer: D. Proportion
Explanation: A proportion is formed when two ratios represent the same relationship and have equal values.
Q. Which of the following ratios is equivalent to 3 : 4?
A. 5 : 6
B. 6 : 8
C. 8 : 10
D. 9 : 15
Answer: B. 6 : 8
Explanation: Equivalent ratios are created by multiplying or dividing both terms by the same number. Here, 3 : 4 multiplied by 2 gives 6 : 8.
Q. Which situation represents a proportional relationship?
A. Two quantities changing without any pattern
B. Two unrelated quantities
C. Two quantities maintaining a constant ratio
D. Two numbers always having the same value
Answer: C. Two quantities maintaining a constant ratio
Explanation: In a proportional relationship, quantities change while keeping the same ratio between them.
Q. If two quantities are in inverse proportion, which condition remains true?
A. x + y remains constant
B. x × y remains constant
C. x − y remains constant
D. x and y are always equal
Answer: B. x × y remains constant
Explanation: In inverse proportion, when one quantity increases, the other decreases, but their product remains constant.
Q. If 4 notebooks cost ₹80, what will be the cost of 8 notebooks?
A. ₹120
B. ₹140
C. ₹160
D. ₹200
Answer: C. ₹160
Explanation: The number of notebooks and their cost are directly proportional. When the quantity doubles, the total cost also doubles.
Q. Which example shows an inverse proportional relationship?
A. More products bought and more total cost
B. More workers completing the same work in less time
C. More distance covered in more time at the same speed
D. More marks resulting in a higher percentage
Answer: B. More workers completing the same work in less time
Explanation: The number of workers and time required for the same work are inversely proportional because more workers reduce the time needed.
Q. If 5 workers complete a task in 10 days, how many days will 10 workers take for the same task?
A. 5 days
B. 10 days
C. 15 days
D. 20 days
Answer: A. 5 days
Explanation: Workers and time are inversely proportional. When the number of workers doubles, the time required becomes half.
Q. A mixture contains milk and water in the ratio 3 : 5. What is the total number of parts?
A. 5
B. 6
C. 8
D. 10
Answer: C. 8
Explanation: Total parts in a ratio are calculated by adding all terms. Here, 3 + 5 = 8.
Q. If a recipe requires sugar and flour in the ratio 2 : 3, how much flour is needed for 6 cups of sugar?
A. 6 cups
B. 8 cups
C. 9 cups
D. 12 cups
Answer: C. 9 cups
Explanation: The ratio 2 : 3 means for every 2 parts of sugar, 3 parts of flour are needed. For 6 cups of sugar, flour required is 9 cups.
Q. What happens to time when speed increases for covering the same distance?
A. Time increases
B. Time decreases
C. Time becomes zero
D. Time remains fixed
Answer: B. Time decreases
Explanation: For a fixed distance, speed and time are inversely proportional. Higher speed reduces the time taken.
Q. If a vehicle travels 150 km in 3 hours, how much distance will it cover in 6 hours at the same speed?
A. 200 km
B. 250 km
C. 300 km
D. 350 km
Answer: C. 300 km
Explanation: Distance and time are directly proportional at the same speed. Doubling the time doubles the distance travelled.
Q. The method of finding the value of one quantity first is known as:
A. Square method
B. Area method
C. Unit method
D. Random method
Answer: C. Unit method
Explanation: The unit method finds the value of one unit first and then uses it to calculate other values.
Q. If 5 pens cost ₹75, what is the cost of one pen?
A. ₹10
B. ₹15
C. ₹20
D. ₹25
Answer: B. ₹15
Explanation: Using the unit method, the cost of one pen = ₹75 ÷ 5 = ₹15.
Q. Which symbol is used to represent a ratio?
A. +
B. =
C. :
D. ×
Answer: C. :
Explanation: The colon symbol (:) is commonly used to show a ratio between quantities.
Q. If two ratios form a proportion, their cross products will be:
A. Equal
B. Always different
C. Zero
D. Negative
Answer: A. Equal
Explanation: Cross multiplication is used to check proportions. Equal cross products mean the ratios are proportional.
Q. On a map, 1 cm represents 20 km. Which mathematical concept is used here?
A. Addition
B. Scale relationship
C. Random comparison
D. Subtraction
Answer: B. Scale relationship
Explanation: Map scales use proportional reasoning to compare map measurements with actual distances.
Q. Which concept is used to show the ratio between map distance and actual distance?
A. Representative fraction
B. Prime number
C. Square number
D. Whole number
Answer: A. Representative fraction
Explanation: Representative fraction represents the relationship between distance on a map and the actual ground distance.
Q. If 4 machines make 80 items in a fixed time, how many items can 8 machines make in the same time?
A. 120
B. 140
C. 160
D. 200
Answer: C. 160
Explanation: Machines and production have a direct relationship. Doubling the machines doubles the production.
Q. In direct proportion, two quantities:
A. Change together in the same direction
B. Always become zero
C. Always move in opposite directions
D. Have no relationship
Answer: A. Change together in the same direction
Explanation: In direct proportion, both quantities increase or decrease together while maintaining the same relationship.
Q. Which mathematical concept is mostly used while increasing or decreasing recipe quantities?
A. Geometry
B. Probability
C. Proportion
D. Data handling
Answer: C. Proportion
Explanation: Proportion helps maintain the same relationship between ingredients when the quantity of a recipe changes.
Q. If 10 chocolates cost ₹50, what will be the cost of 20 chocolates?
A. ₹80
B. ₹90
C. ₹100
D. ₹120
Answer: C. ₹100
Explanation: The number of chocolates and total cost are directly proportional. Doubling chocolates doubles the cost.
Q. In inverse proportion, if one quantity becomes double, the other quantity:
A. Also doubles
B. Becomes half
C. Remains unchanged
D. Becomes zero
Answer: B. Becomes half
Explanation: In inverse proportion, quantities change oppositely while keeping their product constant.
Q. A scale factor helps us to:
A. Compare proportional quantities
B. Count numbers only
C. Find only addition
D. Measure only time
Answer: A. Compare proportional quantities
Explanation: A scale factor explains how a quantity changes while maintaining the same proportion.
Q. Proportional Reasoning II mainly improves:
A. Drawing ability only
B. Memorising answers only
C. Logical comparison skills
D. Guessing ability
Answer: C. Logical comparison skills
Explanation: Proportional reasoning develops the ability to compare quantities and solve real-life mathematical problems.
Q. Divide 15 items in the ratio 1 : 2. What is the larger part?
A. 5
B. 8
C. 10
D. 12
Answer: C. 10
Explanation: Total parts = 3. One part = 15 ÷ 3 = 5. The larger part is 2 × 5 = 10.
Q. Speed and time for a fixed distance have which relationship?
A. Direct proportion
B. Inverse proportion
C. Equal value always
D. No relationship
Answer: B. Inverse proportion
Explanation: When speed increases, time decreases for the same distance. This shows inverse proportion.
Q. If fewer workers are available for the same work, the time required will:
A. Increase
B. Decrease
C. Stay the same
D. Become zero
Answer: A. Increase
Explanation: Workers and time are inversely proportional. Fewer workers need more time to complete the same work.
Q. Solving Proportional Reasoning 2 MCQs regularly helps students improve:
A. Only memorisation
B. Mathematical understanding and accuracy
C. Drawing speed only
D. Guessing skills only
Answer: B. Mathematical understanding and accuracy
Explanation: Regular MCQ practice improves conceptual understanding, calculation skills, and confidence in solving Maths problems.
Important Points Before Practicing MCQs
Before attempting questions from Proportional Reasoning 2, remember these important concepts:
- A ratio is used to compare two or more quantities.
- Equivalent ratios represent the same relationship in different forms.
- A proportion shows that two ratios are equal.
- In direct proportion, two quantities increase or decrease together.
- In inverse proportion, one quantity increases while the other decreases.
- The unit method helps solve real-life problems by finding the value of one unit first.
Common Mistakes Students Make in Chapter 3 Proportional Reasoning 2
Understanding concepts correctly is important while solving Proportional Reasoning 2 questions. Here are some common mistakes students should avoid:
- Confusing Direct and Inverse Proportion: Many students find it difficult to identify whether a question is based on direct or inverse proportion.
Remember: If both quantities increase or decrease together, it is direct proportion. If one quantity increases and the other decreases, it is inverse proportion. - Writing Ratios in the Wrong Order: The order of numbers in a ratio matters. Changing the order can completely change the meaning of the comparison.
For example, the ratio 2 : 5 is different from 5 : 2. Always read the question carefully before writing the ratio. - Forgetting to Simplify Ratios: Sometimes students compare ratios without converting them into their simplest form.
Simplifying ratios makes it easier to identify equivalent relationships and solve questions correctly. - Calculation Errors in Word Problems: Small mistakes in multiplication or division can lead to incorrect answers.
Students should solve questions step by step and check their calculations before selecting an answer. - Ignoring Units While Comparing Quantities: Different units cannot be compared directly. Convert quantities into the same unit whenever required.
For example, kilometres and metres should be converted before making comparisons.
Chapter 3 Proportional Reasoning 2 Preparation Strategy
Proportional Reasoning II becomes easier when students focus on understanding concepts instead of only memorising steps.
Follow these simple preparation tips:
- Revise Basic Concepts First: Start with the meaning of ratio, proportion, and equivalent ratios. Strong basics help in solving advanced questions easily.
- Understand the Relationship Between Quantities: Before solving any question, identify how the given quantities are connected.
- Ask yourself:
- Are both quantities increasing together?
- Is one quantity increasing while the other decreases?
- This helps you decide between direct and inverse proportion.
- Practice Textbook Examples: Examples from Ganita Prakash help students understand the correct method of solving different types of proportional reasoning problems.
- Solve Different Types of MCQs: Practice concept-based, calculation-based, and application-based questions. This improves speed and prepares students for different exam patterns.
- Review Your Mistakes: After solving questions, check incorrect answers carefully. Understanding mistakes helps improve accuracy in future attempts.
