Proportional Reasoning-2 — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 10
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 10, "Proportional Reasoning-2". 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-2", 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-2, 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-2 — important questions & MCQs with answers (Class 8 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
On a map with scale 1 : 1000, 1 cm on the map represents:
A.1 cmB.1000 cm on the ground✓ CorrectC.100 cmD.10 cmAnswer: B. 1000 cm on the ground
Explanation: A scale of 1 : 1000 means 1 map unit equals 1000 real units of the same kind, so 1 cm on the map stands for 1000 cm on the ground — not 100 cm, which would be a scale of 1 : 100.
- Q2Easy
The ratio 2 : 4 : 6 in simplest form is:
A.1 : 2 : 3✓ CorrectB.2 : 4 : 6C.1 : 2 : 4D.2 : 3 : 4Answer: A. 1 : 2 : 3
Explanation: Divide every term by the common factor 2: 2÷2 : 4÷2 : 6÷2 = 1 : 2 : 3. Simplifying a ratio means dividing all terms by the same number, not just some of them.
- Q3Easy
In inverse proportion, when one quantity increases, the other:
A.increasesB.stays the sameC.decreases✓ CorrectD.doublesAnswer: C. decreases
Explanation: Inversely proportional quantities move in opposite directions: as one increases, the other decreases, keeping their product constant.
- Q4Easy
A full pie chart (a complete circle) represents:
A.half the dataB.a quarterC.the whole (100%)✓ CorrectD.10%Answer: C. the whole (100%)
Explanation: A full circle in a pie chart always represents the entire data set, i.e. 100%, never a fraction like half or a quarter of it.
- Q5Easy
On a map with scale 1 : 50000, 1 cm represents how many metres?
A.50 mB.500 m✓ CorrectC.5000 mD.5 mAnswer: B. 500 m
Explanation: 1 cm represents 50000 cm on the ground; dividing by 100 to convert to metres gives 500 m, not 5000 m or 50 m, which come from a misplaced decimal.
- Q6Easy
In the ratio 1 : 2 : 3, how many equal parts are there in all?
A.6✓ CorrectB.5C.3D.7Answer: A. 6
Explanation: The total number of equal parts is the sum of the ratio terms: 1 + 2 + 3 = 6, not just the number of terms in the ratio, which is 3.
- Q7Medium
A map has scale 1 : 200000. A 3 cm distance on the map is:
A.6 km✓ CorrectB.600 kmC.6 mD.60 kmAnswer: A. 6 km
Explanation: Multiply the map length by the scale factor: 3 cm × 200000 = 600000 cm, which converts to 6 km. Forgetting to convert centimetres to kilometres gives a mismatched unit like 6 m.
- Q8Medium
Divide ₹600 in the ratio 1 : 2 : 3. The three shares are:
A.₹200, ₹200, ₹200B.₹100, ₹200, ₹300✓ CorrectC.₹150, ₹200, ₹250D.₹120, ₹180, ₹300Answer: B. ₹100, ₹200, ₹300
Explanation: The ratio 1 : 2 : 3 has 6 equal parts, each worth ₹600 ÷ 6 = ₹100, giving shares of ₹100, ₹200 and ₹300 — not equal shares of ₹200 each, which ignores the ratio.
- Q9Medium
6 workers build a wall in 8 days. How long will 12 workers take?
A.4 days✓ CorrectB.16 daysC.24 daysD.2 daysAnswer: A. 4 days
Explanation: Workers × days stays constant for a fixed job: 6 × 8 = 48, so with 12 workers it takes 48 ÷ 12 = 4 days — doubling the workers halves the days, it doesn't double them to 16.
- Q10Medium
In a pie chart, a category with 30% has a sector angle of:
A.30°B.90°C.120°D.108°✓ CorrectAnswer: D. 108°
Explanation: Convert percentage to angle by multiplying by 3.6° per percent: 30% × 3.6° = 108°. Writing 30° directly confuses the percentage figure with the angle.
- Q11Medium
The real distance is 25 km. On a scale of 1 cm : 5 km, the map length is:
A.25 cmB.125 cmC.1 cmD.5 cm✓ CorrectAnswer: D. 5 cm
Explanation: Divide the real distance by what each centimetre represents: 25 km ÷ 5 km per cm = 5 cm. Multiplying instead (25 × 5 = 125) confuses distance with scale factor.
- Q12Hard
₹3500 is divided among A, B, C where A : B = 2 : 3 and B : C = 4 : 5. A's share is:
A.₹1200B.₹800✓ CorrectC.₹1500D.₹700Answer: B. ₹800
Explanation: Scaling both ratios to a common B (=12) gives A : B : C = 8 : 12 : 15, or 35 equal parts of ₹100 each, so A's 8 parts are 8 × 100 = ₹800 — not ₹1200, from combining the ratios incorrectly.
- Q13Hard
12 workers finish a task in 10 days. How many workers are needed to finish it in 8 days?
A.9.6B.16C.15✓ CorrectD.20Answer: C. 15
Explanation: Workers × days is constant: 12 × 10 = 120, so finishing in 8 days needs 120 ÷ 8 = 15 workers — fewer days means more workers, not fewer, ruling out 9.6.
- Q14Hard
A pie chart has sectors of 25%, 35% and one more. The third sector's angle is:
A.144°✓ CorrectB.40°C.60°D.216°Answer: A. 144°
Explanation: The two known sectors total 25% + 35% = 60%, so the third is 100% − 60% = 40%, which as an angle is 40% × 3.6° per percent = 144° — not 40°, which confuses percentage with angle.
Key concepts: Proportional Reasoning-2 (Class 8 Mathematics)
This chapter deepens proportional reasoning. Alongside direct proportion it introduces inverse proportion, where two quantities move in opposite directions and their product stays constant — as with speed and time, or workers and days. You also read map scales, work with ratios of three or more terms, divide a whole in a given ratio, and turn data into a pie chart, where every sector's angle is proportional to the value it stands for.
- Direct proportion (recap)
- Two quantities in direct proportion increase or decrease together and their ratio stays constant: double the amount, double the cost.
- Inverse proportion
- Two quantities in inverse proportion move in opposite directions — as one increases the other decreases — and their product stays constant, like speed and time for a fixed distance.
- The x₁y₁ = x₂y₂ rule
- For inversely proportional quantities the product is fixed, so x₁ × y₁ = x₂ × y₂; this solves problems like '6 workers, 8 days → 12 workers, ? days'.
- Speed and time
- For a fixed distance, speed × time is constant, so travelling faster takes proportionally less time — a classic inverse proportion.
- Workers and time
- The total work (workers × days) is fixed, so more workers finish in fewer days and fewer workers take longer.
- Map scale
- A ratio comparing map distance to real distance; on a 1 : 50000 map, 1 cm stands for 50000 cm = 500 m, so real = map length × scale.
- Multi-term ratio
- A ratio like a : b : c compares three quantities at once; 2 : 4 : 6 simplifies to 1 : 2 : 3, and the parts add to give the total number of shares.
- Dividing a whole in a ratio
- Split the total into (a + b + c) equal parts and give each item its number of parts: ₹600 in 1 : 2 : 3 gives ₹100, ₹200, ₹300.
- Pie chart
- A circle divided into sectors so that each sector's angle is proportional to its value; the whole circle (360°) represents 100% of the data.
- Sector angle
- The angle of a category equals (its value ÷ the total) × 360°, so a 30% category takes up 108°.
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Start this chapter free →Proportional Reasoning-2 — FAQs
What are the key concepts in Class 8 Mathematics Proportional Reasoning-2?+
This chapter deepens proportional reasoning. Alongside direct proportion it introduces inverse proportion, where two quantities move in opposite directions and their product stays constant — as with speed and time, or workers and days. You also read map scales, work with ratios of three or more terms, divide a whole in a given ratio, and turn data into a pie chart, where every sector's angle is proportional to the value it stands for. Key ideas include Direct proportion (recap), Inverse proportion, The x₁y₁ = x₂y₂ rule, Speed and time, Workers and time, Map scale.
What does Class 8 Mathematics Chapter 10 (Proportional Reasoning-2) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "Proportional Reasoning-2": 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-2" questions free to practise?+
Yes. Sign in with Google to practise "Proportional Reasoning-2" 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-2" 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-2" 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-2" 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-2 (Class 8 Mathematics)?+
The questions that matter most test Direct proportion (recap), Inverse proportion, The x₁y₁ = x₂y₂ rule, Speed and time, Workers and time, Map scale. 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-2?+
Yes — Class 8 Mathematics Proportional Reasoning-2 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.