Proportional Reasoning-1 — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 7
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 7, "Proportional Reasoning-1". You get 9 timed quizzes made from 72 NCERT-based MCQs, with answers and explanations. The questions are split into 24 Easy, 24 Medium and 24 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams get right.
To score well in "Proportional Reasoning-1", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Proportional Reasoning-1, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 8 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Proportional Reasoning-1 — important questions & MCQs with answers (Class 8 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
The ratio 6 : 9 written in simplest form is:
A.2 : 3✓ CorrectB.3 : 2C.6 : 9D.1 : 3Answer: A. 2 : 3
Explanation: Divide both terms by their HCF, 3: 6÷3 : 9÷3 = 2 : 3. Do not flip the order — 3 : 2 is a different ratio.
- Q2Easy
If 2 pens cost ₹10, one pen costs:
A.₹20B.₹8C.₹5✓ CorrectD.₹2Answer: C. ₹5
Explanation: Divide the total cost by the number of pens to get the unit cost: ₹10 ÷ 2 = ₹5.
- Q3Easy
Two ratios that are equal form a:
A.fraction onlyB.sumC.differenceD.proportion✓ CorrectAnswer: D. proportion
Explanation: When two ratios are equal, such as 2 : 3 and 4 : 6, together they form a proportion.
- Q4Easy
The ratio 10 : 15 written in simplest form is:
A.3 : 2B.10 : 15C.2 : 3✓ CorrectD.5 : 3Answer: C. 2 : 3
Explanation: Divide both terms by their HCF, 5: 10÷5 : 15÷5 = 2 : 3, not 3 : 2 — keep the terms in the order given.
- Q5Easy
If 3 apples cost ₹30, the cost of 1 apple is:
A.₹90B.₹10✓ CorrectC.₹3D.₹27Answer: B. ₹10
Explanation: Divide the total cost by the number of apples for the unit cost: ₹30 ÷ 3 = ₹10.
- Q6Easy
Which ratio is equivalent to 1 : 2?
A.5 : 10✓ CorrectB.2 : 1C.3 : 4D.1 : 3Answer: A. 5 : 10
Explanation: Multiply both terms of 1 : 2 by the same number, 5, to get the equivalent ratio 5 : 10.
- Q7Medium
Convert 2.5 metres to centimetres.
A.25 cmB.2500 cmC.250 cm✓ CorrectD.2.5 cmAnswer: C. 250 cm
Explanation: Since 1 m = 100 cm, multiply by 100: 2.5 × 100 = 250 cm, not 25 cm, which comes from dividing instead.
- Q8Medium
If 5 books cost ₹200, then 8 books cost:
A.₹250B.₹320✓ CorrectC.₹300D.₹160Answer: B. ₹320
Explanation: Find the unit cost first: ₹200 ÷ 5 = ₹40 per book, then scale up: 40 × 8 = ₹320.
- Q9Medium
If x : 8 = 3 : 4, find x.
A.5B.6✓ CorrectC.12D.2Answer: B. 6
Explanation: Cross-multiply: 4 × x = 3 × 8 = 24, so x = 24 ÷ 4 = 6.
- Q10Medium
Divide ₹100 between two people in the ratio 3 : 2. The larger share is:
A.₹40B.₹50C.₹60✓ CorrectD.₹30Answer: C. ₹60
Explanation: There are 3 + 2 = 5 equal parts worth ₹100 ÷ 5 = ₹20 each, so the larger share is 3 × 20 = ₹60.
- Q11Medium
Convert 3000 grams to kilograms.
A.30 kgB.3 kg✓ CorrectC.0.3 kgD.3000 kgAnswer: B. 3 kg
Explanation: Since 1000 g = 1 kg, divide by 1000: 3000 ÷ 1000 = 3 kg.
- Q12Hard
If A : B = 2 : 3 and B : C = 4 : 5, then A : C is:
A.2 : 5B.6 : 20C.8 : 15✓ CorrectD.5 : 8Answer: C. 8 : 15
Explanation: Scale both ratios so B matches: A : B = 8 : 12 and B : C = 12 : 15, giving A : C = 8 : 15.
- Q13Hard
If 8 pens cost ₹96, how many pens can be bought for ₹156?
A.12B.14C.11D.13✓ CorrectAnswer: D. 13
Explanation: One pen costs ₹96 ÷ 8 = ₹12, so ₹156 buys 156 ÷ 12 = 13 pens.
- Q14Hard
If 3 : 5 = 12 : x, find x.
A.14B.20✓ CorrectC.10D.60Answer: B. 20
Explanation: Cross-multiply: 3 × x = 5 × 12 = 60, so x = 60 ÷ 3 = 20.
Key concepts: Proportional Reasoning-1 (Class 8 Mathematics)
This chapter is about comparing quantities that change together. A ratio compares two quantities by division, and equal ratios form a proportion. You learn to write ratios in simplest form, find equivalent ratios, and check proportions by cross-multiplication. The unitary method — first find the value of one unit, then scale up — solves direct-proportion problems, and you also share a quantity in a given ratio and convert between units, keeping quantities in the same units throughout.
- Ratio
- A comparison of two quantities of the same kind by division, written a : b and read 'a to b'. For 4 boys and 6 girls the ratio is 4 : 6.
- Simplest form of a ratio
- A ratio in which the two terms have no common factor except 1, found by dividing both terms by their HCF: 6 : 9 becomes 2 : 3.
- Same units first
- The two quantities in a ratio must be in the same unit before comparing, so 45 minutes to 1 hour is 45 : 60 = 3 : 4, not 45 : 1.
- Equivalent ratios
- Ratios with the same value, obtained by multiplying or dividing both terms by the same number: 1 : 2 = 5 : 10 = 50 : 100.
- Proportion
- A statement that two ratios are equal, such as 2 : 3 = 4 : 6. The four quantities are said to be in proportion.
- Cross-multiplication rule
- In a proportion a : b = c : d, the product of the extremes equals the product of the means: a × d = b × c. This finds a missing term.
- Unitary method
- First find the value of one unit by dividing, then multiply for the number required: if 5 kg cost ₹250 then 1 kg is ₹50 and 8 kg is ₹400.
- Direct proportion
- Two quantities in direct proportion increase or decrease together so their ratio stays constant: double the cloth, double the cost.
- Dividing in a ratio
- To share a quantity in the ratio a : b, split it into (a + b) equal parts and give a parts to one share and b to the other.
- Proportional change / scaling
- Enlarging or reducing a figure multiplies every length by the same scale factor, so the shape stays similar — a 2 cm length becoming 6 cm has scale factor 3.
- Unit conversion
- Changing units uses fixed ratios: 1 m = 100 cm, 1 kg = 1000 g, and 72 km/h = 72 × 5/18 = 20 m/s.
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Start this chapter free →Proportional Reasoning-1 — FAQs
What are the key concepts in Class 8 Mathematics Proportional Reasoning-1?+
This chapter is about comparing quantities that change together. A ratio compares two quantities by division, and equal ratios form a proportion. You learn to write ratios in simplest form, find equivalent ratios, and check proportions by cross-multiplication. The unitary method — first find the value of one unit, then scale up — solves direct-proportion problems, and you also share a quantity in a given ratio and convert between units, keeping quantities in the same units throughout. Key ideas include Ratio, Simplest form of a ratio, Same units first, Equivalent ratios, Proportion, Cross-multiplication rule.
What does Class 8 Mathematics Chapter 7 (Proportional Reasoning-1) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "Proportional Reasoning-1": 24 Easy, 24 Medium and 24 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams.
Are these "Proportional Reasoning-1" questions free to practise?+
Yes. Sign in with Google to practise "Proportional Reasoning-1" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 8 till 31 March; on 1 April your account moves up to Class 9 and the rest of your year carries over. No chapter is charged separately.
How should I revise "Proportional Reasoning-1" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Proportional Reasoning-1" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Proportional Reasoning-1" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Proportional Reasoning-1 (Class 8 Mathematics)?+
The questions that matter most test Ratio, Simplest form of a ratio, Same units first, Equivalent ratios, Proportion, Cross-multiplication rule. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 72 questions on the chapter as timed quizzes.
Is there an online quiz for Proportional Reasoning-1?+
Yes — Class 8 Mathematics Proportional Reasoning-1 has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.