Explore how ratios describe image sizes, mixtures, prices and shared quantities in Class 8 Maths, Ganita Prakash Part 1, Chapter 7: Proportional Reasoning-1. These MCQs with answers and explanations include equivalent ratios, unit rates, proportional sharing and everyday applications. The questions also distinguish scaling from adding equal amounts, helping you decide which relationships preserve a ratio and which change it.
Class 8 Maths Ganita Prakash Part 1 Chapter 7 MCQs with Answers
Set 1: Ratio Basics, Image Scaling and Proportion MCQs (Questions 1–5)
Q1. An image is 60 mm wide and 40 mm high. What is the ratio of its width to its height in simplest form?
[A]. 2 : 1
[B]. 3 : 1
[C]. 3 : 2
[D]. 2 : 3
Q2. A 60 mm wide and 40 mm high image is resized without changing its shape. Which pair of new dimensions is possible?
[A]. Width 90 mm, height 40 mm
[B]. Width 60 mm, height 60 mm
[C]. Width 90 mm, height 60 mm
[D]. Width 40 mm, height 20 mm
Q3. An image has width 60 mm and height 40 mm. Both dimensions are reduced by 20 mm. What is the new width-to-height ratio, and does the shape remain unchanged?
[A]. 1 : 1; no
[B]. 2 : 1; no
[C]. 2 : 1; yes
[D]. 3 : 2; yes
Q4. Which statement of proportion is true?
[A]. 12 : 18 :: 28 : 12
[B]. 8 : 3 :: 24 : 6
[C]. 4 : 7 :: 12 : 21
[D]. 7 : 12 :: 12 : 7
Set 2: Ratios in Mixtures, Ages and Quantities MCQs (Questions 6–10)
Q6. Regular coffee contains 15 mL of coffee decoction and 35 mL of milk. Which mixture has exactly the same decoction-to-milk ratio?
[A]. 10 mL decoction and 40 mL milk
[B]. 30 mL decoction and 60 mL milk
[C]. 20 mL decoction and 30 mL milk
[D]. 24 mL decoction and 56 mL milk
Q7. Kesang uses 10 spoons of sugar for 6 glasses of lemonade. How many more spoons are needed for 18 additional glasses with the same sweetness? Assume all glasses and spoonfuls are equal in size.
[A]. 30 spoons
[B]. 20 spoons
[C]. 40 spoons
[D]. 18 spoons
Q8. Nitin uses 3 bags of cement for 60 ft of wall, and Hari uses 2 bags for 40 ft. What is the wall length per bag for each person? Assume all cement bags have the same mass.
[A]. Nitin: 60 ft; Hari: 40 ft
[B]. Nitin: 30 ft; Hari: 20 ft
[C]. Nitin: 20 ft; Hari: 20 ft
[D]. Nitin: 20 ft; Hari: 30 ft
Q9. When Neelima was 3 years old, her mother was 30 years old. What is the ratio of Neelima’s age to her mother’s age when Neelima is 12?
[A]. 4 : 13
[B]. 2 : 5
[C]. 3 : 10
[D]. 1 : 10
Q10. A cook prepares 15 kg of rice for 120 students. How much rice is needed for 80 students if the quantity per student stays the same?
[A]. 20 kg
[B]. 22.5 kg
[C]. 10 kg
[D]. 12 kg
Set 3: Cross Products, Travel and Price Comparisons MCQs (Questions 11–15)
Q11. For positive numbers a, b, c and d, which equality must hold when a : b :: c : d?
[A]. a × d = b × c
[B]. a × c = b × d
[C]. a + d = b + c
[D]. a × b = c × d
Q12. A car travels 90 km in 150 minutes at a constant speed. How far will it travel in 4 hours at the same speed?
[A]. 240 km
[B]. 144 km
[C]. 360 km
[D]. 96 km
Q13. One tea packet contains 200 g and costs ₹200. Another contains 1 kg and costs ₹800. How much more does 1 kg of the first tea cost than 1 kg of the second tea? Assume the first tea is bought at the stated packet price.
[A]. ₹600
[B]. ₹800
[C]. ₹1,000
[D]. ₹200
Q14. A motorcyclist completes a journey in 2 hours at 50 km/h. How long will the same journey take at a constant speed of 75 km/h?
[A]. 120 minutes
[B]. 180 minutes
[C]. 150 minutes
[D]. 80 minutes
Q15. A 6 mL shampoo sachet costs ₹2, while a 180 mL bottle costs ₹154. What is the cost of buying 180 mL in sachets at the stated price?
[A]. ₹60
[B]. ₹154
[C]. ₹90
[D]. ₹30
Set 4: Sharing, Pricing and Mixture Ratios MCQs (Questions 16–20)
Q16. Asha and Ravi share 42 counters in the ratio 4 : 3. How many counters do Asha and Ravi receive, respectively?
[A]. 24 and 18
[B]. 28 and 14
[C]. 21 and 21
[D]. 18 and 24
Q17. Prashanti invests ₹75,000 and Bhuvan invests ₹25,000 in a business. They share a profit of ₹4,000 in the ratio of their investments. What is Prashanti’s share?
[A]. ₹1,000
[B]. ₹2,000
[C]. ₹3,000
[D]. ₹3,500
Q18. Land costs ₹15,00,000 per acre, and 1 acre = 43,560 square feet. At the same rate, what is the cost of 2,400 square feet, rounded to the nearest rupee?
[A]. ₹62,500
[B]. ₹8,26,446
[C]. ₹1,50,000
[D]. ₹82,645
Q19. A 240 mL mixture contains acid and water in the ratio 1 : 5. How much acid does it contain?
[A]. 48 mL
[B]. 120 mL
[C]. 40 mL
[D]. 200 mL
Q20. A 40 mL paint mixture contains blue and yellow paint in the ratio 3 : 5. Another 20 mL of yellow paint is added. What is the new blue-to-yellow ratio?
[A]. 3 : 5
[B]. 1 : 3
[C]. 3 : 7
[D]. 1 : 2
Set 5: Mixtures, Conversions and Ratio Applications MCQs (Questions 21–25)
Q21. One full bucket of orange paint contains red and yellow paint in the ratio 3 : 5. One equally large full bucket of yellow paint is added. What is the new ratio of red paint to yellow paint?
[A]. 3 : 10
[B]. 3 : 13
[C]. 3 : 8
[D]. 3 : 5
Q22. A 40 kg mixture contains sand and cement in the ratio 3 : 1. How much cement must be added to make the sand-to-cement ratio 5 : 2?
[A]. 10 kg
[B]. 4 kg
[C]. 12 kg
[D]. 2 kg
Q23. The temperature conversion rule is F = (9/5) × C + 32, where C and F are the Celsius and Fahrenheit readings. What is 25°C in Fahrenheit?
[A]. 57°F
[B]. 77°F
[C]. 45°F
[D]. 68°F
Q24. Three buses of equal capacity carry 162 people when every seat is occupied. What is the minimum number of these buses needed for 204 people, and how many seats will remain empty?
[A]. 4 buses; 12 empty seats
[B]. 4 buses; 42 empty seats
[C]. 3 buses; no empty seats
[D]. 5 buses; 66 empty seats
Q25. A crane’s height is 155 cm. Its neck length and the length of the rest of its body are in the ratio 4 : 6. What is its neck length?
[A]. 38.75 cm
[B]. 77.5 cm
[C]. 93 cm
[D]. 62 cm
Set 6: Ratios, Rates and a Logic Puzzle MCQs (Questions 26–30)
Q26. Harmain is 1 year old and her brother is 5 years old. How old will Harmain be when the ratio of her age to her brother’s age is 1 : 2?
[A]. 5 years
[B]. 4 years
[C]. 2 years
[D]. 3 years
Q27. A tap fills a 500 mL mug in 15 seconds. At the same flow rate, how long will it take to fill an empty 10-litre bucket?
[A]. 200 seconds
[B]. 600 seconds
[C]. 150 seconds
[D]. 300 seconds
Q28. Equal volumes of gold and water have masses in the ratio 37 : 2. If 1 litre of water has a mass of 1 kg, what mass of gold does this ratio give for 1 litre?
[A]. 2 kg
[B]. 37 kg
[C]. 18.5 kg
[D]. 74 kg
Q29. A pair of oxen takes 6 hours to plough 1 acre. A tractor works at four times the oxen’s rate. At these constant rates, how long will the tractor take to plough 20 acres?
[A]. 30 hours
[B]. 480 hours
[C]. 120 hours
[D]. 80 hours
Q30. In a 6-cell Binairo row, H represents a horizontal mark and V a vertical mark. A row must have three H marks and three V marks, with no three identical marks consecutive. Which sequence satisfies both rules?
[A]. H V H V H H
[B]. H H V H V V
[C]. H H H V V V
[D]. H V V V H H
Part 1 Chapter 7: Full Chapter MCQs (Set 1)
Q31. What is the minimum number of moves needed to turn a triangle of 10 coins upside down?
[A]. 1 move
[B]. 2 moves
[C]. 3 moves
[D]. 4 moves
Q32. What characteristic makes digital images appear similar even if they are of different sizes?
[A]. All images must be square.
[B]. The widths and heights have changed by the same factor.
[C]. The images are rotated.
[D]. They have the same color palette.
Q33. What is used in mathematics to represent proportional relationships?
[A]. Difference
[B]. Sum
[C]. Ratio
[D]. Product
Q34. In a ratio of the form a:b, what do ‘a’ and ‘b’ represent?
[A]. The product of two quantities.
[B]. The terms of the ratio.
[C]. The sum of two quantities.
[D]. The difference between two quantities.
Part 1 Chapter 7: Full Chapter MCQs (Set 2)
Q35. How can ratios be reduced to their simplest form?
[A]. By adding their terms.
[B]. By subtracting their terms.
[C]. By multiplying their terms.
[D]. By dividing the terms by their HCF.
Q36. When are two ratios considered to be in proportion, or proportional?
[A]. When their terms are added together.
[B]. When their simplest forms are the same.
[C]. When they use different units.
[D]. When their terms are multiplied.
Q37. Kesang made lemonade with 6 glasses of lemonade and 10 spoons of sugar. If she needs to make 18 more glasses to maintain the same sweetness, how many spoons of sugar should she add?
[A]. 30 spoons
[B]. 18 spoons
[C]. 60 spoons
[D]. 10 spoons
Q38. Nitin built a 60 ft wall using 3 bags of cement, and Hari built a 40 ft wall using 2 bags of cement. Is Nitin correct in worrying that Hari’s wall would be less strong?
[A]. Yes, because Hari used less cement.
[B]. No, because both walls are equally strong.
[C]. Only if the walls are of different heights.
[D]. It depends on the type of cement used.
Part 1 Chapter 7: Full Chapter MCQs (Set 3)
Q39. When the same number is added to (or subtracted from) the terms of a ratio, does the ratio necessarily remain proportional to the original ratio?
[A]. Yes, always.
[B]. No, it changes and is not necessarily proportional.
[C]. Only if the added number is zero.
[D]. It depends on the initial ratio.
Q40. What is the fundamental principle used to solve problems where four quantities are linked proportionally, with three known and one unknown?
[A]. Subtraction
[B]. Addition
[C]. Proportional reasoning
[D]. Factoring
Q41. If a:b::c:d, what algebraic relationship holds true between the terms?
[A]. a + d = b + c
[B]. a – d = b – c
[C]. ad = bc
[D]. a⁄b = c⁄d
Q42. In ancient India, what were problems of proportionality called by Aryabhata and others?
[A]. Rule of Four
[B]. Rule of Three problems
[C]. Proportion Problems
[D]. Cross-Multiplication Rules
Part 1 Chapter 7: Full Chapter MCQs (Set 4)
Q43. According to Aryabhata’s “Rule of Three,” if ‘pramāņa’ is ‘a’, ‘phala’ is ‘b’, and ‘ichchhā’ is ‘c’, how is ‘ichchhāphala’ (d) calculated?
[A]. pramāņa × phala ÷ ichchhā
[B]. phala × ichchhā ÷ pramāņa
[C]. ichchhā + phala – pramāņa
[D]. pramāņa × ichchhā ÷ phala
Q44. A car travels 90 km in 150 minutes. If it continues at the same speed, what distance will it cover in 4 hours?
[A]. 90 km
[B]. 144 km
[C]. 240 km
[D]. 60 km
Q45. Himachal tea sells for ₹200 per 200 g packet, and Meghalaya tea sells for ₹800 per 1 kg packet. Which tea is more expensive?
[A]. Meghalaya tea
[B]. Himachal tea
[C]. Both are equally expensive.
[D]. Cannot be determined without more information.
Q46. If a quantity ‘x’ is to be divided in the ratio m:n, what are the expressions for the two parts?
[A]. m × (m + n) and n × (m + n)
[B]. m⁄x and n⁄x
[C]. m × (x⁄(m + n)) and n × (x⁄(m + n))
[D]. x ÷ m and x ÷ n
Part 1 Chapter 7: Full Chapter MCQs (Set 5)
Q47. Prashanti invested ₹75,000 and Bhuvan invested ₹25,000 in a business. If they gain a profit of ₹4,000, how much profit does Prashanti get if they share it in the ratio of their investment?
[A]. ₹1,000
[B]. ₹2,000
[C]. ₹3,000
[D]. ₹4,000
Q48. A mixture of 40 kg contains sand and cement in the ratio of 3:1. How much cement should be added to make the ratio of sand to cement 5:2?
[A]. 5 kg
[B]. 10 kg
[C]. 2 kg
[D]. 12 kg
Q49. If 1 metre equals 3.281 feet, how many square feet are in 1 square metre?
[A]. 3.281 square feet
[B]. 10.764 square feet
[C]. 1 square foot
[D]. 0.3048 square feet
Q50. How is temperature converted from Fahrenheit to Celsius?
[A]. Celsius = (9⁄5) × Fahrenheit + 32
[B]. Celsius = (5⁄9) × Fahrenheit – 32
[C]. Celsius = (5⁄9) × (Fahrenheit – 32)
[D]. Celsius = Fahrenheit – 32 × (5⁄9)
Choose the Right Comparison Before Calculating
Before setting up a ratio, put comparable measurements in the same units and identify what stays fixed. For sharing problems, find the total number of parts; for rates, find the amount per unit. Revisit the age and mixture questions to explain why adding equal amounts may change a ratio.
