Important Questions and Answers for Class 8 Maths Chapter 3 Proportional Reasoning-2 2025-26

1. Multiple choice questions.

1. If 2 cups of rice and 1 cup of urad dal are mixed, what is the ratio of rice to urad dal?

• (a) 1 : 2
• (b) 2 : 1
• (c) 1 : 3
• (d) 3 : 2

Answer: (b) 2 : 1

2. Which of the following represents an inverse proportion?

• (a) Speed and distance travelled in a fixed time
• (b) Time taken and speed to cover a fixed distance
• (c) Time and number of students eating food together
• (d) Distance and time at constant speed

Answer: (b) Time taken and speed to cover a fixed distance

3. In a mixture, the ratio of cement : sand : gravel is 1 : 1.5 : 3. If you have 3 bags of cement, how many bags of sand are needed?

• (a) 4.5
• (b) 3
• (c) 1.5
• (d) 9

Answer: (a) 4.5

2. Very Short Answer (VSA).

1. What is a proportional relationship?

Answer: A proportional relationship exists when two or more related quantities change by the same factor, and their ratios remain constant.

2. Define Representative Fraction (RF) as used in maps.

Answer: Representative Fraction (RF) shows the ratio of a distance on the map to the corresponding actual distance on the ground.

3. What does it mean if two ratios are proportional?

Answer: Two ratios are proportional if their cross-products are equal; that is, $a:b::c:d$ if $a \times d = b \times c$.

4. Give an example of a ratio with more than two terms.

Answer: The ratio 8 : 4 : 2 : 1, representing coriander seeds, red chillies, toor dal, and fenugreek seeds in a spice mix, is a ratio with more than two terms.

3. Short Answer Questions.

1. How much cement, sand, and gravel are needed to make 110 units of concrete in the ratio 1 : 1.5 : 3?

Answer:

• Total parts = 1 + 1.5 + 3 = 5.5
• Each unit multiplier = $110 ÷ 5.5 = 20$
• Cement = $1 × 20 = 20$ units; Sand = $1.5 × 20 = 30$ units; Gravel = $3 × 20 = 60$ units

2. How do you check if two ratios with more than two terms are proportional?

Answer: For ratios with several terms, compare each term: $a/p = b/q = c/r = d/s$. If all these ratios are equal, then $a : b : c : d$ and $p : q : r : s$ are proportional.

3. If a triangle's angles are in the ratio 1 : 3 : 5, find the value of each angle.

Answer:

• Sum of ratios = 1 + 3 + 5 = 9
• $\angle A = 180 \times 1/9 = 20°$
• $\angle B = 180 \times 3/9 = 60°$
• $\angle C = 180 \times 5/9 = 100°$

4. How are the quantities of ingredients determined for maintaining the same taste in mixtures with different initial amounts?

Answer: The quantities must be scaled proportionally. For example, if one ingredient is halved, all others should be halved to maintain the same ratio and thus the same taste.

5. Explain inverse proportion with a real life example from the chapter.

Answer: If the number of workers increases to complete a job, the number of days needed decreases in the same proportion. For instance, doubling workers halves days needed, showing inverse proportionality.

4. True or False Questions.

1. The sum of the terms in any ratio gives the total number of parts into which the whole is divided.

Answer: True

2. Inverse proportion means increasing one quantity increases the other too.

Answer: False

3. Ratios in maps are used to convert distances on maps to real-life distances.

Answer: True

4. In a ratio 3 : 4, doubling both numbers keeps the ratio unchanged.

Answer: True

3. Fill in the Blanks Questions.

1. Two quantities x and y vary in inverse proportion if their product x × y = ______.

Answer: constant (k)

2. When dividing 12 in the ratio 2 : 1, the first part is ______ and the second part is ______.

Answer: 8; 4

3. The ratio of coriander seeds to red chillies to toor dal to fenugreek seeds in Viswanath's spice mix is ______.

Answer: 8 : 4 : 2 : 1

4. In a pie chart, the total angle of the circle is ______ degrees.

Answer: 360

5. If Ram and Shyam work together and finish their work in 3/5 hours, working alone Ram takes ______ hour and Shyam takes ______ hours respectively.

Answer: 1; 1.5

Why Proportional Reasoning Helps in Maths

Learning proportional reasoning 2 class 8 solutions pdf develops logical thinking and calculation skills. Concepts from proportional reasoning 2 class 8 extra questions prepare you well for class 8 maths chapter proportional reasoning 2 exams. These are vital for understanding ratios, inverse proportions, and map scales.

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By working through proportional reasoning-1 class 8 and algebra play class 8 solutions, you develop a solid foundation for advanced mathematics. These resources guide you in understanding both direct and inverse relationships, essential for later studies and daily life maths situations.