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CBSE Class 8  >  Class 8 Notes  >  Mathematics (Maths)   >  MCQ (with Solutions): Direct and Inverse Proportions

MCQ (with Solutions): Direct and Inverse Proportions

Q1: 10 meters of cloth cost Rs 1000. What will 4 meters cost?
(a) Rs 400
(b) Rs 800
(c) Rs 200
(d) Rs 100

Q2: If x = 20 and y = 40, then x and y are:
(a) Directly proportional
(b)  Inversely proportional
(c) Neither directly nor inversely proportional
(d) Cannot be determined 

Q3: If x and y are directly proportional, then which of the following is correct?
(a) x+y=constant
(b) x-y=constant
 (c) xy=constant
(d) x/y=constant 

Q4: The weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2500 grams?
(a) 750
(b) 800
(c) 850
(d) 950 

Q5: If x and y are inversely proportional, then which one is true?
(a) x1/y1 = x2/y2
(b) x1 /x2 = y1/y2
(c) x1 /x2 = y2/y1
(d) x1 .x2 = y1.y2 

Q6: If 12 workers can build a wall in 50 hours, how many workers will be required to do the same work in 40 hours?
(a) 10
(b) 13
(c) 14
(d) 15 

Q7: If 300 Kg of coal cost 6000₹, then find the cost of 120 kg of coal?
(a) 1200₹
(b) 2400₹
(c) 3200₹
(d) 4200₹ 

Q8: If it takes 40 days for 120 men to complete a work, how long will it take for 80 men to complete the same work?
(a) 50 days
(b) 60 days
(c) 80 days
(d) 100 days

Q9: A car takes 18 hours to ride 720 kilometers. Time taken by the car to travel 360 kilometers is:
(a) 10 hours
(b) 11 hours
(c) 9 hours
(d) 16 hours

Q10: The scale of a map is given as 1: 300. Two cities are 4 km apart on the map. The actual distance between them is:
(a) 1000 km
(b) 1100 km
(c) 1200 km
(d) 1300 km 

Q11: If 5 kg of apples cost ₹300, what will 8 kg cost (assuming price varies directly)?
​(a) ₹400
​(b) ₹450
​(c) ₹480
​(d) ₹500

Q12: A car travels 120 km in 3 hours. How far will it travel in 5 hours?
​(a) 150 km
(b) 180 km
(c) 200 km
(d) 220 km

Q13: 6 pumps can empty a tank in 8 hours. How long will 4 pumps take?
​(a) 10 hours
(b) 12 hours
(c) 14 hours
(d) 16 hours

Q14: If x and y are directly proportional, and x = 9 when y = 27, what will y be when x = 6?
​(a) 12
(b) 15
(c) 18
(d) 20

Q15: A job takes 15 days for 3 workers. How many days will 5 workers take?

(a) 6 days
(b) 8 days
(c) 9 days
(d) 10 days

The document MCQ (with Solutions): Direct and Inverse Proportions is a part of the Class 8 Course Mathematics (Maths) Class 8.
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FAQs on MCQ (with Solutions): Direct and Inverse Proportions

1. What's the difference between direct proportion and inverse proportion with examples?
Ans. Direct proportion means when one quantity increases, the other increases at the same rate (like cost and number of items). Inverse proportion means when one quantity increases, the other decreases proportionally (like speed and time to travel a fixed distance). In direct proportion, the ratio stays constant; in inverse proportion, the product stays constant. Understanding these relationships helps solve real-world problems efficiently in Class 8 Mathematics.
2. How do I identify whether a problem is direct or inverse proportion before solving it?
Ans. Read the problem carefully to determine the relationship between variables. If increasing one quantity leads to increasing the other at the same rate, it's direct proportion. If increasing one causes the other to decrease, it's inverse proportion. Key indicator words include "more...more" for direct and "more...less" for inverse relationships. Recognising these patterns quickly helps students select the correct formula and method for MCQ-based questions.
3. Why do we use the constant of proportionality (k) in both direct and inverse proportion problems?
Ans. The constant of proportionality (k) represents the fixed relationship between two quantities. In direct proportion, y = kx means the ratio y/x always equals k. In inverse proportion, y = k/x means the product xy always equals k. This constant allows students to find unknown values and verify solutions systematically, making it essential for solving MCQ questions with accuracy.
4. What mistakes do students commonly make when solving direct and inverse proportion MCQs?
Ans. Common errors include confusing the two types and using wrong formulas, forgetting to find k before calculating unknowns, and miscalculating when ratios involve fractions or decimals. Students also sometimes assume proportionality without checking actual relationships. Reviewing MCQ solutions carefully and practising with varied examples helps avoid these mistakes during exams and builds confidence in proportion concepts.
5. Can a single real-life scenario involve both direct and inverse proportions simultaneously?
Ans. Yes, complex situations often combine both types. For example, in work-related problems, the number of workers and time taken show inverse proportion, while total work done and workers show direct proportion. Recognising these dual relationships in CBSE Mathematics Class 8 MCQs requires careful analysis. Breaking the problem into separate proportion relationships and solving each methodically ensures accuracy in mixed-type questions.
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