Direct and Inverse Proportions — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 111
Pre-2026 syllabusThis chapter is from the older NCERT book. See the 2026-27 Class 8 Mathematics chapters →
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 111, "Direct and Inverse Proportions". 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 set top scorers in CBSE Board exams apart.
To score well in "Direct and Inverse Proportions", 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 trains you to stay accurate under time pressure, 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 Direct and Inverse Proportions, 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.
Key concepts: Direct and Inverse Proportions (Class 8 Mathematics)
This chapter covers direct and inverse proportion and how to use them to solve real-life problems including time-and-work.
- Direct proportion
- Two quantities are in direct proportion if they increase or decrease together so that x/y stays constant.
- Inverse proportion
- Two quantities are in inverse proportion if one increases as the other decreases so that their product xy stays constant.
- Identifying the type
- Decide whether more of one means more (direct) or less (inverse) of the other before solving.
- Time and work
- More workers take less time — an inverse-proportion application.
Direct and Inverse Proportions — important questions & MCQs with answers (Class 8 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 58 are timed and scored when you sign in.
- Q1Easy
If x and y are in direct proportion:
A.x/y is constant✓ CorrectB.xy is constantC.x+y is constantD.x−y is constantAnswer: A. x/y is constant
Explanation: y = kx; ratio constant.
- Q2Easy
Inverse proportion: as x increases, y:
A.IncreasesB.Decreases (xy = constant)✓ CorrectC.Stays sameD.RandomAnswer: B. Decreases (xy = constant)
Explanation: xy = k.
- Q3Easy
Which pair of quantities is in DIRECT proportion?
A.Number of taps and time to fill a tankB.Speed of a car and time to cover a fixed distanceC.Number of pens bought and total cost✓ CorrectD.Number of workers and days to finish a fixed jobAnswer: C. Number of pens bought and total cost
Explanation: More pens means proportionally more cost, so cost/pens stays constant — direct proportion.
- Q4Easy
Which pair of quantities is in INVERSE proportion?
A.Length of cloth and its costB.Weight of sugar and its priceC.Distance travelled and petrol usedD.Number of workers and time to build a wall✓ CorrectAnswer: D. Number of workers and time to build a wall
Explanation: More workers finish the wall in less time, so workers × time is constant — inverse proportion.
- Q5Easy
If 4 kg of rice costs ₹240, the cost of 7 kg at the same rate is:
A.₹420✓ CorrectB.₹360C.₹480D.₹400Answer: A. ₹420
Explanation: Per kg = 240 ÷ 4 = 60; for 7 kg, 60 × 7 = ₹420.
- Q6Easy
In inverse proportion between x and y, which product stays the same for all matching values?
A.x ÷ yB.x − yC.x × y✓ CorrectD.x + yAnswer: C. x × y
Explanation: For inverse proportion x × y = k, a constant.
- Q7Medium
5 books cost ₹250. Cost of 8 books:
A.₹450B.₹350C.₹500D.₹400✓ CorrectAnswer: D. ₹400
Explanation: (250/5)·8 = 400.
- Q8Medium
6 workers complete a job in 10 days. 12 workers will take:
A.5 days✓ CorrectB.20 daysC.15 daysD.6 daysAnswer: A. 5 days
Explanation: More workers → less time (inverse). 6·10 = 12·t ⇒ t=5.
- Q9Medium
On a map, 1 cm represents 8 km. Two towns 5.5 cm apart on the map are actually:
A.40 kmB.42 kmC.44 km✓ CorrectD.48 kmAnswer: C. 44 km
Explanation: Map distance and real distance are directly proportional: 5.5 × 8 = 44 km.
- Q10Medium
8 taps fill a tank in 27 minutes. How long will 12 taps of the same size take?
A.16 minutesB.18 minutes✓ CorrectC.24 minutesD.20 minutesAnswer: B. 18 minutes
Explanation: Taps × time is constant: 8 × 27 = 12 × t ⇒ t = 216 ÷ 12 = 18 minutes.
- Q11Medium
A 6-litre tin of paint covers 90 m² of wall. How much paint is needed for 240 m²?
A.15 litresB.16 litres✓ CorrectC.14 litresD.18 litresAnswer: B. 16 litres
Explanation: Coverage per litre = 90 ÷ 6 = 15 m²; 240 ÷ 15 = 16 litres.
- Q12Hard
If 3 m of cloth costs ₹150, then ₹500 will buy:
A.7.5 mB.8 mC.6 mD.10 m✓ CorrectAnswer: D. 10 m
Explanation: Per m = 50; 500/50 = 10 m.
- Q13Hard
A car at 60 km/h takes 5 h. At 75 km/h, time:
A.3 hB.6 hC.4 h✓ CorrectD.5.5 hAnswer: C. 4 h
Explanation: 60·5 = 75·t ⇒ t = 4.
- Q14Hard
x and y are in direct proportion with the pairs (4, 10), (6, 15), (10, ?). Which statement is INCORRECT?
A.The constant of proportionality y/x is 2.5B.When x = 10, y = 25C.When y = 20, x = 8D.The product xy is the same for every pair✓ CorrectAnswer: D. The product xy is the same for every pair
Explanation: In direct proportion the ratio y/x is constant, not the product xy, so saying xy is constant is incorrect.
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Start this chapter free →Direct and Inverse Proportions — FAQs
What are the key concepts in Class 8 Mathematics Direct and Inverse Proportions?+
This chapter covers direct and inverse proportion and how to use them to solve real-life problems including time-and-work. Key ideas include Direct proportion, Inverse proportion, Identifying the type, Time and work.
What does Class 8 Mathematics Chapter 111 (Direct and Inverse Proportions) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "Direct and Inverse Proportions": 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 "Direct and Inverse Proportions" questions free to practise?+
Yes. Sign in with Google to practise "Direct and Inverse Proportions" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Direct and Inverse Proportions" 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 "Direct and Inverse Proportions" 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 "Direct and Inverse Proportions" 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 Direct and Inverse Proportions (Class 8 Mathematics)?+
The questions that matter most test Direct proportion, Inverse proportion, Identifying the type, Time and work. This page shows 14 solved important MCQs with answers and explanations; all 72 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Direct and Inverse Proportions?+
Yes — Class 8 Mathematics Direct and Inverse Proportions 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.