CBSE Class 8 Maths Chapter 7: Proportional Reasoning-1 — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 7: Proportional Reasoning - 1 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): Two shapes are scaled proportionally when all corresponding lengths change by the same factor.
Reason (R): A common scale factor preserves their shape without distortion.
Reason (R): A common scale factor preserves their shape without distortion.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Equal multiplicative change maintains corresponding ratios.
2
Assertion (A): Similar images can have different sizes.
Reason (R): The ratio 6:9 simplifies to 2:3.
Reason (R): The ratio 6:9 simplifies to 2:3.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the numerical simplification does not explain the images' similarity.
3
Assertion (A): Stretching only an image's width generally destroys similarity.
Reason (R): Unequal horizontal and vertical scale factors preserve every ratio.
Reason (R): Unequal horizontal and vertical scale factors preserve every ratio.
Answer: (c)
A is true, but R is false. Unequal scaling distorts the width-to-height ratio.
4
Assertion (A): Two images with equal widths must be similar.
Reason (R): Their heights and all corresponding proportions may still differ.
Reason (R): Their heights and all corresponding proportions may still differ.
Answer: (d)
A is false, but R is true. One matching length is insufficient.
5
Assertion (A): A ratio compares two quantities by division.
Reason (R): The order of the quantities matters in writing the ratio.
Reason (R): The order of the quantities matters in writing the ratio.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. a:b and b:a generally represent different comparisons.
6
Assertion (A): The ratios 6:9 and 2:3 are equivalent.
Reason (R): A unitary method first finds the value for one unit.
Reason (R): A unitary method first finds the value for one unit.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the unitary-method definition does not explain this ratio equivalence.
7
Assertion (A): The simplest form of 18:24 is 3:4.
Reason (R): The ratio 9:12 cannot be simplified further.
Reason (R): The ratio 9:12 cannot be simplified further.
Answer: (c)
A is true, but R is false. Both terms of 9:12 are divisible by 3.
8
Assertion (A): Dividing only one term of a ratio by 2 preserves the ratio.
Reason (R): Equivalent ratios require the same nonzero factor on both terms.
Reason (R): Equivalent ratios require the same nonzero factor on both terms.
Answer: (d)
A is false, but R is true. Changing one term alters the comparison.
9
Assertion (A): If a:b = c:d, then ad = bc.
Reason (R): Cross multiplication expresses equality of the two fractions a/b and c/d.
Reason (R): Cross multiplication expresses equality of the two fractions a/b and c/d.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Multiplying by bd gives the cross-product equality.
10
Assertion (A): The ratios 4:6 and 10:15 are proportional.
Reason (R): The ratios 3:4 and 6:7 are not proportional.
Reason (R): The ratios 3:4 and 6:7 are not proportional.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the second comparison does not explain the first.
11
Assertion (A): The ratios 5:8 and 15:20 are not proportional.
Reason (R): Their cross-products are equal.
Reason (R): Their cross-products are equal.
Answer: (c)
A is true, but R is false. The products are 100 and 120, so they differ.
12
Assertion (A): A ratio has units that must always remain different.
Reason (R): When like quantities are compared, converting to the same units gives a unit-free ratio.
Reason (R): When like quantities are compared, converting to the same units gives a unit-free ratio.
Answer: (d)
A is false, but R is true. Unit conversion is necessary for a valid like-quantity comparison.
13
Assertion (A): A unitary method first finds the value corresponding to one unit.
Reason (R): That unit value can then be multiplied to find other required values.
Reason (R): That unit value can then be multiplied to find other required values.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The two-step reasoning scales from one to many.
14
Assertion (A): If 4 pens cost 60 at a fixed rate, one pen costs 15.
Reason (R): Seven pens then cost 105.
Reason (R): Seven pens then cost 105.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the seven-pen result follows after rather than explains the unit cost.
15
Assertion (A): At a fixed rate of 60 per kg, 5 kg of rice costs 300.
Reason (R): It costs 240.
Reason (R): It costs 240.
Answer: (c)
A is true, but R is false. Five times 60 equals 300.
16
Assertion (A): At a fixed rate, doubling quantity halves total cost.
Reason (R): Cost and quantity increase in the same ratio.
Reason (R): Cost and quantity increase in the same ratio.
Answer: (d)
A is false, but R is true. They are directly proportional, so doubling quantity doubles cost.
17
Assertion (A): To divide a total in the ratio m:n, the total is split into m + n equal parts.
Reason (R): The two shares contain m and n of those parts respectively.
Reason (R): The two shares contain m and n of those parts respectively.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This construction preserves the required ratio and total.
18
Assertion (A): Dividing 70 in the ratio 2:5 gives shares 20 and 50.
Reason (R): The total number of ratio parts is 7.
Reason (R): The total number of ratio parts is 7.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the part count alone does not state the completed shares.
19
Assertion (A): Dividing 96 in the ratio 1:3 gives shares 32 and 64.
Reason (R): One ratio part equals 96/4 = 24.
Reason (R): One ratio part equals 96/4 = 24.
Answer: (c)
A is true, but R is false. The shares are 24 and 72.
20
Assertion (A): A conversion factor may be applied to the numerical value without considering its direction.
Reason (R): Converting back requires the reciprocal factor.
Reason (R): Converting back requires the reciprocal factor.
Answer: (d)
A is false, but R is true. Multiplication direction determines whether units grow or shrink.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 7 Proportional Reasoning-1?
This chapter covers all key topics from Proportional Reasoning-1 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-1 online for free?
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