CBSE Class 8 Maths Chapter 10: Proportional Reasoning-2 — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 10: Proportional Reasoning - 2 from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): The ratios a:b and c:d are proportional when ad = bc.
Reason (R): Cross-multiplication tests whether the two ratios represent the same relative relationship.
Reason (R): Cross-multiplication tests whether the two ratios represent the same relative relationship.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Equality of cross-products is equivalent to a/b = c/d for nonzero denominators.
2
Assertion (A): The ratios 6:3 and 4:2 are proportional.
Reason (R): A map scale is commonly written as a ratio.
Reason (R): A map scale is commonly written as a ratio.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the map-scale fact does not explain the equality of these ratios.
3
Assertion (A): The ratios 2:3 and 8:12 are proportional.
Reason (R): Their cross-products are unequal.
Reason (R): Their cross-products are unequal.
Answer: (c)
A is true, but R is false. Both cross-products equal 24.
4
Assertion (A): The ratios 3:5 and 9:20 are proportional.
Reason (R): Their cross-products are 60 and 45.
Reason (R): Their cross-products are 60 and 45.
Answer: (d)
A is false, but R is true. Unequal cross-products show that the assertion is false.
5
Assertion (A): A map scale of 1:100000 means 1 unit on the map represents 100000 of the same units on the ground.
Reason (R): A scale is a proportional relationship between map distance and actual distance.
Reason (R): A scale is a proportional relationship between map distance and actual distance.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Keeping units consistent gives the stated interpretation.
6
Assertion (A): At scale 1:50000, 2 cm on a map represents 1 km on the ground.
Reason (R): The ratio 2:3:5 has 10 total parts.
Reason (R): The ratio 2:3:5 has 10 total parts.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the multipart ratio does not explain the map conversion.
7
Assertion (A): A ratio 2:3:5 has 10 total parts.
Reason (R): The total number of parts is found by multiplying 2 x 3 x 5.
Reason (R): The total number of parts is found by multiplying 2 x 3 x 5.
Answer: (c)
A is true, but R is false. The parts are added: 2 + 3 + 5 = 10.
8
Assertion (A): Dividing 120 in the ratio 2:3 gives shares 24 and 96.
Reason (R): The two shares should be 48 and 72.
Reason (R): The two shares should be 48 and 72.
Answer: (d)
A is false, but R is true. Each part is 120/5 = 24; the shares are 2 x 24 and 3 x 24.
9
Assertion (A): Angles in the ratio 1:3:5 can form a triangle with angles 20, 60 and 100 degrees.
Reason (R): The nine ratio parts must total 180 degrees, so each part is 20 degrees.
Reason (R): The nine ratio parts must total 180 degrees, so each part is 20 degrees.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The resulting angles add to 180 degrees.
10
Assertion (A): Side lengths in a fixed ratio produce similar triangles when a triangle is possible.
Reason (R): Triangles with the same three side lengths are congruent.
Reason (R): Triangles with the same three side lengths are congruent.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but congruence at one scale does not explain similarity across different scales.
11
Assertion (A): Side lengths in the ratio 1:3:5 cannot form a triangle.
Reason (R): The two smaller parts add to more than the largest part.
Reason (R): The two smaller parts add to more than the largest part.
Answer: (c)
A is true, but R is false. They add to 4, which is less than 5, so the triangle inequality fails.
12
Assertion (A): In a pie chart, a sector's angle is unrelated to its share of the whole.
Reason (R): The central angle is proportional to the represented quantity.
Reason (R): The central angle is proportional to the represented quantity.
Answer: (d)
A is false, but R is true. A larger share receives a proportionally larger angle.
13
Assertion (A): Directly proportional quantities change by the same factor.
Reason (R): Their ratio remains constant.
Reason (R): Their ratio remains constant.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Multiplying both corresponding values by the same factor preserves the ratio.
14
Assertion (A): If 3 notebooks cost 90 at a fixed rate, 5 notebooks cost 150.
Reason (R): For inverse proportion, the product of corresponding values is constant.
Reason (R): For inverse proportion, the product of corresponding values is constant.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the inverse-proportion rule does not explain this direct-proportion calculation.
15
Assertion (A): If y is directly proportional to x, doubling x halves y.
Reason (R): For direct proportion, y/x remains constant.
Reason (R): For direct proportion, y/x remains constant.
Answer: (c)
A is true, but R is false. Doubling x doubles y when the constant is unchanged.
16
Assertion (A): The time for a fixed journey is directly proportional to speed.
Reason (R): At fixed distance, increasing speed reduces travel time.
Reason (R): At fixed distance, increasing speed reduces travel time.
Answer: (d)
A is false, but R is true. Speed and time are inversely proportional.
17
Assertion (A): For inversely proportional positive quantities x and y, the product xy is constant.
Reason (R): Multiplying x by a factor requires dividing y by the same factor.
Reason (R): Multiplying x by a factor requires dividing y by the same factor.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Those opposite changes preserve the product.
18
Assertion (A): If 6 workers take 10 days for fixed work at equal rates, 12 workers take 5 days.
Reason (R): A map scale compares map and ground distances.
Reason (R): A map scale compares map and ground distances.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the map fact does not explain the worker-time relationship.
19
Assertion (A): If x and y are inversely proportional and x doubles, y also doubles.
Reason (R): The product xy must remain fixed.
Reason (R): The product xy must remain fixed.
Answer: (c)
A is true, but R is false. To keep the product fixed, y must halve.
20
Assertion (A): Every pair of quantities that changes together is proportional.
Reason (R): A proportional relationship must maintain a constant ratio or constant product, as appropriate.
Reason (R): A proportional relationship must maintain a constant ratio or constant product, as appropriate.
Answer: (d)
A is false, but R is true. Co-variation alone is insufficient.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 10 Proportional Reasoning-2?
This chapter covers all key topics from Proportional Reasoning-2 as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Proportional Reasoning-2 online for free?
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