Work with map scales, mixtures, pie charts and changing work rates in Class 8 Maths, Ganita Prakash Part 2, Chapter 3: Proportional Reasoning–2. These MCQs with answers and explanations extend ratio reasoning to several quantities and distinguish direct from inverse proportion. Each set develops a different application, from dividing a total into parts to finding sector angles and calculating how long a fixed task takes.
Class 8 Maths Ganita Prakash Part 2 Chapter 3 MCQs with Answers
Set 1: Equivalent Ratios, Map Scales and Recipes MCQs (Questions 1–5)
Q1. Viswanath mixes 6 cups of rice with 3 cups of urad dal. Puneet mixes 4 cups of rice with 2 cups of urad dal. Which statement correctly compares their rice-to-dal ratios?
[A]. The ratios cannot be compared
[B]. Both ratios equal 2 : 1
[C]. Viswanath’s ratio is greater
[D]. Puneet’s ratio is greater
Q2. For positive quantities a, b, c, and d, the ratios a : b and c : d are proportional. Which formula gives d?
[A]. d = ab/c
[B]. d = bc/a
[C]. d = ac/b
[D]. d = a + b − c
Q3. A map has a Representative Fraction of 1 : 60,00,000. What actual geographical distance does 1 cm on the map represent?
[A]. 60 km
[B]. 6 km
[C]. 60,000 km
[D]. 600 km
Q4. A classroom plan is drawn at a scale of 1 : 50. A line on the plan is 2 cm long. What actual length does it represent?
[A]. 25 cm
[B]. 2.5 cm
[C]. 50 cm
[D]. 100 cm
Q5. A spice mix contains 8 spoons of coriander seeds, 4 red chillies, 2 spoons of toor dal, and 1 spoon of fenugreek seeds. With only 2 red chillies, what quantities of coriander seeds, toor dal, and fenugreek seeds preserve the same proportions?
[A]. 8 spoons, 2 spoons, 1 spoon
[B]. 4 spoons, 1 spoon, 0.5 spoon
[C]. 2 spoons, 1 spoon, 0.5 spoon
[D]. 4 spoons, 2 spoons, 1 spoon
Set 2: Ratios in Mixtures and Triangle Angles MCQs (Questions 6–10)
Q6. Red, blue, and white paints are mixed in the ratio 2 : 3 : 5. Yasmin has 10 litres of white paint. How much red paint and blue paint should she add?
[A]. 2 litres red and 3 litres blue
[B]. 6 litres red and 4 litres blue
[C]. 4 litres red and 6 litres blue
[D]. 5 litres red and 5 litres blue
Q7. Cement, sand, and gravel are measured in equal-sized bags in the ratio 1 : 1.5 : 3. If 3 bags of cement are used, what is the total number of bags of ingredients?
[A]. 13.5 bags
[B]. 16.5 bags
[C]. 5.5 bags
[D]. 9 bags
Q8. A total of 110 units is divided among cement, sand, and gravel in the ratio 1 : 1.5 : 3. What are the three quantities, respectively?
[A]. 10, 30, and 70 units
[B]. 20, 40, and 50 units
[C]. 20, 30, and 60 units
[D]. 30, 20, and 60 units
Q9. A 50 ml mixture of red, blue, and white paint has the ratio 2 : 3 : 5. How much blue paint does it contain?
[A]. 25 ml
[B]. 30 ml
[C]. 10 ml
[D]. 15 ml
Q10. The angles of a triangle are in the ratio 1 : 3 : 5. What is its largest angle?
[A]. 120°
[B]. 60°
[C]. 100°
[D]. 90°
Set 3: Ratio Sharing and Triangle Properties MCQs (Questions 11–15)
Q11. A 150-minute cricket practice session divides time among warm-up/cool-down, batting, bowling, and fielding in the ratio 3 : 4 : 3 : 5. How much time is allotted to fielding?
[A]. 30 minutes
[B]. 75 minutes
[C]. 40 minutes
[D]. 50 minutes
Q12. A school library has Odia, Hindi, and English books in the ratio 3 : 2 : 1. It has 288 Odia books. How many Hindi and English books does it have, respectively?
[A]. 96 and 192
[B]. 192 and 96
[C]. 576 and 288
[D]. 144 and 96
Q13. There are 100 coins. The numbers of ₹10, ₹5, ₹2, and ₹1 coins are in the ratio 4 : 3 : 2 : 1. What is their total value?
[A]. ₹500
[B]. ₹100
[C]. ₹600
[D]. ₹1,000
Q14. Can a triangle have side lengths in the ratio 1 : 3 : 5?
[A]. Yes, because all three terms are positive
[B]. No, because every triangle must have three equal sides
[C]. Yes, because the ratio has three terms
[D]. No, because the sum of the two shorter sides is less than the longest side
Q15. Two triangles each have side lengths in the ratio 3 : 4 : 5. Must the triangles be congruent?
[A]. No, because the same ratio can describe triangles of different sizes
[B]. Yes, because equal ratios force equal lengths
[C]. Yes, because both have three sides
[D]. No, because no triangle can have this ratio
Set 4: Simplifying Ratios and Reading Pie Charts MCQs (Questions 16–20)
Q16. The numbers of students receiving grades A, B, C, D, and E are 12, 10, 8, 6, and 4. What is this five-term ratio in its simplest form?
[A]. 12 : 5 : 4 : 3 : 2
[B]. 6 : 10 : 4 : 6 : 2
[C]. 6 : 5 : 4 : 3 : 2
[D]. 3 : 2 : 2 : 1 : 1
Q17. In a class of 40 students, 12 receive grade A. What central angle represents grade A in a pie chart?
[A]. 108°
[B]. 120°
[C]. 12°
[D]. 90°
Q18. Of 360 people surveyed, 90 prefer summer and 120 prefer the rainy season. Everyone else prefers winter. What central angle represents winter in a pie chart?
[A]. 150°
[B]. 120°
[C]. 210°
[D]. 90°
Q19. In a survey of favourite TV channels, 15% of viewers choose news. What angle should represent news in the pie chart?
[A]. 150°
[B]. 36°
[C]. 54°
[D]. 15°
Q20. A school transport pie chart has angles of 90° for walking, 60° for cycling, 120° for bus travel, and 60° for two-wheeler travel. The remaining sector represents 18 children travelling by car. How many children were surveyed?
[A]. 360
[B]. 108
[C]. 216
[D]. 180
Set 5: Direct and Inverse Proportion MCQs (Questions 21–25)
Q21. Five workers move 4,500 bricks in one day. How many workers are needed to move 18,000 bricks in one day, if every worker works at the same constant rate for the same number of hours?
[A]. 25
[B]. 15
[C]. 10
[D]. 20
Q22. Positive quantities x and y vary in inverse proportion. Which expression remains constant?
[A]. xy
[B]. x − y
[C]. x + y
[D]. x/y
Q23. The quantities x and y are inversely proportional. When x = 16, y = 9. What is y when x = 36?
[A]. 4
[B]. 12
[C]. 6
[D]. 20.25
Q24. A journey takes 3 hours at a constant speed of 30 km/h. How long will the same journey take at a constant speed of 60 km/h, with no stops?
[A]. 0.5 hour
[B]. 6 hours
[C]. 1.5 hours
[D]. 2 hours
Q25. Twenty workers lay a road in 4 days. How many days will 10 workers take for the same road, assuming equal constant work rates and the same working hours each day?
[A]. 8 days
[B]. 4 days
[C]. 2 days
[D]. 10 days
Set 6: Inverse Proportion and Combined Work Rates MCQs (Questions 26–30)
Q26. Food provisions can feed 80 students for 15 days. If 20 more students join, how long will the provisions last, assuming the same daily amount of food per student and no additional supplies?
[A]. 15 days
[B]. 12 days
[C]. 18.75 days
[D]. 10 days
Q27. Ram cuts a quantity of vegetables in 1 hour, while Shyam cuts the same quantity in 1.5 hours. At their constant individual rates, how many minutes will they take if they work together without interfering with each other?
[A]. 90 minutes
[B]. 60 minutes
[C]. 75 minutes
[D]. 36 minutes
Q28. Chairs are arranged in 25 rows with 12 chairs in each row. If all the same chairs are rearranged with 20 chairs in each row, how many rows are formed?
[A]. 30
[B]. 40
[C]. 20
[D]. 15
Q29. A school has 8 periods of 45 minutes each. If the same total teaching time is divided into 9 equal periods, how long is each period?
[A]. 40 minutes
[B]. 45 minutes
[C]. 50 minutes
[D]. 35 minutes
Q30. A factory uses 42 machines to make a fixed number of toys in 63 days. How many machines are needed to make the same number in 54 days, assuming equal constant production rates and equal working hours each day?
[A]. 45
[B]. 49
[C]. 54
[D]. 36
Decide Whether the Ratio or Product Stays Constant
For each proportion problem, identify the constant ratio in direct proportion or the constant product in inverse proportion. Check units before applying a map scale. In pie charts, confirm that the sector angles total 360°. For people working together, add their rates of work before finding the time needed for the task.
