Important Questions Class 8 Maths Chapter 7 Proportional Reasoning-1

Proportional reasoning is the method of comparing quantities that change by the same multiplicative factor. Ratios, proportions, sharing, cross multiplication, and unit conversions help students solve real-life comparison problems.

A picture looks similar after resizing only when its width and height change by the same factor. Important Questions Class 8 Maths Chapter 7 help students understand ratios, simplest form, proportional relationships, Rule of Three, sharing in a given ratio, and unit conversions through real examples like images, lemonade, cement walls, filter coffee, mid-day meals, tea packets, paint mixtures, and land measurement. The 2026 NCERT chapter Proportional Reasoning-1 in Ganita Prakash Class 8 uses comparison and scaling as the main idea.

Key Takeaways

• Ratio: A ratio (a : b) means for every (a) units of the first quantity, there are (b) units of the second quantity.
• Proportion: Two ratios are proportional when both reduce to the same simplest form.
• Cross Multiplication: If (a : b :: c : d), then (a \times d = b \times c).
• Sharing In Ratio: A quantity (x) shared in (m : n) gives parts (m × x/(m+n)) and (n × x/(m+n)).

Important Questions Class 8 Maths Chapter 7 Structure 2026

Proportional Reasoning Class 8 Chapter Overview

Proportional reasoning begins when two related quantities change by the same multiplicative factor. The chapter first explains this through resized images, where similar-looking images keep the same width-to-height ratio.

The chapter then moves to ratios, simplest forms, proportions, cross multiplication, Rule of Three, unequal sharing, mixture problems, and unit conversions. Each idea is linked to a practical situation instead of only formula use.

Class 8 Maths Chapter 7 Important Questions On Proportional Reasoning

Proportional reasoning is useful when two quantities grow or shrink together. Students must check multiplication factors, not only addition or subtraction differences.

The chapter uses resized images to show why equal subtraction does not always preserve similarity.

Q1. What Is Proportional Reasoning Class 8?

Proportional reasoning is the method of comparing quantities that change by the same factor.

It helps students check whether two ratios represent the same relationship. This is different from checking whether the quantities have the same difference.

Example: Width 60 mm and height 40 mm become 30 mm and 20 mm. Both are multiplied by (1/2).

Q2. Why Do Some Resized Images Look Similar?

Resized images look similar when width and height change by the same factor.

If only one dimension changes properly, the image becomes stretched or compressed. Similar images keep the same width-to-height ratio.

Example: (60 : 40), (30 : 20), and (90 : 60) all reduce to (3 : 2).

Q3. Why Does Equal Subtraction Not Always Preserve Similarity?

Equal subtraction does not always preserve similarity because proportional change needs multiplication.

If width and height reduce by the same number, their factors may still differ. Different factors distort the shape.

Example: From (60 × 40), reducing both by 20 gives (40 × 20). The new ratio is (2 : 1), not (3 : 2).

Q4. Which Images Are Similar If Their Width-Height Ratios Are 60:40, 30:20, 90:60, 40:20, And 60:60?

The images with ratios 60:40, 30:20, and 90:60 are similar.

1. (60 : 40 = 3 : 2)
2. (30 : 20 = 3 : 2)
3. (90 : 60 = 3 : 2)
4. (40 : 20 = 2 : 1)
5. (60 : 60 = 1 : 1)

Final Answer: 60:40, 30:20, and 90:60 are proportional.

Ratio Class 8 Maths Important Questions

A ratio compares two quantities in a fixed order. The first term and second term must refer to the same order throughout a problem.

Students should always reduce ratios before comparing them.

Q5. What Is A Ratio In Class 8 Maths?

A ratio compares two quantities using the form (a : b).

It means for every (a) units of the first quantity, there are (b) units of the second quantity. The quantities must be in the same unit when needed.

Example: Width 60 mm and height 40 mm give the ratio (60 : 40).

Q6. What Are The Terms Of A Ratio?

The terms of a ratio are the two numbers being compared.

In (a : b), (a) is the first term and (b) is the second term. Their order matters.

Example: In (15 : 35), 15 is coffee decoction and 35 is milk.

Q7. Write The Ratio Of Width To Height For A Rectangle Of Width 90 Mm And Height 60 Mm.

The ratio of width to height is (90 : 60).

1. Width = 90 mm
2. Height = 60 mm
3. Ratio = Width : Height
4. Ratio = (90 : 60)
5. Simplest form = (3 : 2)

Final Answer: (90 : 60 = 3 : 2)

Q8. Why Is Order Important In A Ratio?

Order is important because (a : b) and (b : a) compare different quantities.

If the first term changes, the meaning changes. A ratio of coffee to milk is different from milk to coffee.

Example: (15 : 35) means coffee : milk, while (35 : 15) means milk : coffee.

Ratios In Simplest Form Class 8 Questions

A ratio in simplest form shows the same comparison with the smallest whole-number terms. Students should divide both terms by their HCF.

This method is the safest way to compare ratios.

Q9. How Do You Reduce Ratios In Simplest Form Class 8?

A ratio is reduced to simplest form by dividing both terms by their HCF.

The HCF removes the common factor from both terms. The comparison remains the same.

Example: HCF of 60 and 40 is 20, so (60 : 40 = 3 : 2).

Q10. Reduce 72:96 To Its Simplest Form.

The simplest form of (72 : 96) is (3 : 4).

1. Terms = 72 and 96
2. HCF of 72 and 96 = 24
3. Divide both terms by 24
4. (72 ÷ 24 = 3)
5. (96 ÷ 24 = 4)

Final Answer: (72 : 96 = 3 : 4)

Q11. Reduce 14:21 To Its Simplest Form.

The simplest form of (14 : 21) is (2 : 3).

1. Terms = 14 and 21
2. HCF = 7
3. (14 ÷ 7 = 2)
4. (21 ÷ 7 = 3)

Final Answer: (14 : 21 = 2 : 3)

Q12. Are 60:40 And 90:60 Proportional?

Yes, (60 : 40) and (90 : 60) are proportional.

1. (60 : 40 = 3 : 2)
2. (90 : 60 = 3 : 2)
3. Both ratios have the same simplest form.

Final Answer: Yes, they are proportional.

Proportion Class 8 Maths Questions With Answers

Two ratios are in proportion when they represent the same comparison. The symbol (::) is used to show proportionality.

Students can compare proportions by simplest form or cross multiplication.

Q13. What Is Proportion Class 8 Maths?

Proportion means two ratios are equal or proportional.

It is written as (a : b :: c : d). It means both ratios change by the same factor.

Example: (60 : 40 :: 30 : 20) because both reduce to (3 : 2).

Q14. Are 3:4 And 72:96 Proportional?

Yes, (3 : 4) and (72 : 96) are proportional.

1. (3 : 4) is already in simplest form.
2. HCF of 72 and 96 = 24
3. (72 : 96 = 3 : 4)
4. Both ratios are equal.

Final Answer: Yes, (3 : 4 :: 72 : 96)

Q15. Are 8:3 And 24:6 Proportional?

No, (8 : 3) and (24 : 6) are not proportional.

1. (8 : 3) is in simplest form.
2. (24 : 6 = 4 : 1)
3. (8 : 3) and (4 : 1) are different.

Final Answer: No, they are not proportional.

Q16. Circle The True Proportion: 4:7::12:21 Or 7:12::12:7.

The true proportion is (4 : 7 :: 12 : 21).

1. (12 : 21 = 4 : 7) after dividing by 3.
2. (7 : 12) and (12 : 7) compare opposite quantities.
3. They are not equal ratios.

Final Answer: (4 : 7 :: 12 : 21)

Q17. Give Three Ratios Proportional To 4:9.

Three ratios proportional to (4 : 9) are (8 : 18), (12 : 27), and (20 : 45).

Each ratio is formed by multiplying both terms by the same number. The simplest form stays (4 : 9).

Example: (4 × 5 : 9 × 5 = 20 : 45).

Cross Multiplication Class 8 Questions

Cross multiplication helps test proportions and find unknown values. It works only when the ratios are correctly formed.

Students must keep the same order of quantities in both ratios.

Q18. What Is Cross Multiplication Class 8?

Cross multiplication states that if (a : b :: c : d), then (a × d = b × c).

It helps find the fourth unknown quantity in a proportion. This idea comes from equal ratios.

Example: If (6 : 10 :: 18 : x), then (6x = 180).

Q19. Find x If 6:10::18:x.

The value of (x) is 30.

1. Given proportion: (6 : 10 :: 18 : x)
2. Cross multiply: (6x = 10 × 18)
3. (6x = 180)
4. (x = 180 ÷ 6)
5. (x = 30)

Final Answer: (x = 30)

Q20. Fill The Missing Number: 14:21::28:____

The missing number is 42.

1. (14 : 21 :: 28 : x)
2. 28 is (2 × 14)
3. The second term also doubles.
4. (21 × 2 = 42)

Final Answer: 42

Q21. Fill The Missing Number: 14:21::6:____

The missing number is 9.

1. (14 : 21 :: 6 : x)
2. Factor from 14 to 6 = (6/14 = 3/7)
3. (x = 21 × 3/7)
4. (x = 9)

Final Answer: 9

Q22. Fill The Missing Number: 18:24::20:____

The missing number is (80/3) or (26⅔).

1. (18 : 24 :: 20 : x)
2. Cross multiply: (18x = 24 × 20)
3. (18x = 480)
4. (x = 480 ÷ 18)
5. (x = 80/3)

Final Answer: (80/3) or (26⅔)

Rule Of Three Class 8 And Trairasika Questions

The Rule of Three is used when three quantities are known and the fourth is unknown. The chapter also introduces the ancient Indian name Trairasika for such proportional problems.

The order of quantities must remain consistent before cross multiplication.

Q23. What Is Rule Of Three Class 8?

Rule of Three is a method for finding the fourth quantity when three proportional quantities are known.

It uses the form (a : b :: c : d). The unknown value is found through cross multiplication.

Formula: (d = (b × c) / a)

Q24. What Is Trairasika Class 8?

Trairasika is the ancient Indian Rule of Three method for proportional problems.

It uses pramāṇa, phala, ichchhā, and ichchhāphala. Āryabhaṭa described it as multiplying phala by ichchhā and dividing by pramāṇa.

Formula: ichchhāphala = phala × ichchhā / pramāṇa.

Q25. A Cook Uses 15 Kg Rice For 120 Students. How Much Rice Is Needed For 80 Students?

The cook should make 10 kg of rice.

1. Students : Rice = (120 : 15 :: 80 : x)
2. Cross multiply: (120x = 15 × 80)
3. (120x = 1200)
4. (x = 1200 ÷ 120)
5. (x = 10) kg

Final Answer: 10 kg

Q26. A Car Travels 90 Km In 150 Minutes. How Far Will It Travel In 4 Hours At The Same Speed?

The car will travel 144 km in 4 hours.

1. Convert 4 hours to minutes: (4 × 60 = 240) minutes
2. Time : Distance = (150 : 90 :: 240 : x)
3. Cross multiply: (150x = 240 × 90)
4. (x = 21600 ÷ 150)
5. (x = 144) km

Final Answer: 144 km

Q27. Why Must Units Be Same In Rule Of Three Problems?

Units must be same because ratios compare like quantities.

If one time value is in minutes and another is in hours, the comparison becomes wrong. Convert before forming the proportion.

Example: 4 hours must become 240 minutes before comparing with 150 minutes.

Q28. A Tap Fills 500 mL In 15 Seconds. How Long Will It Take To Fill A 10 Litre Bucket?

The tap will take 300 seconds or 5 minutes.

1. Convert 10 litres to mL: (10 × 1000 = 10000) mL
2. Volume : Time = (500 : 15 :: 10000 : x)
3. Cross multiply: (500x = 150000)
4. (x = 300) seconds
5. (300) seconds = 5 minutes

Final Answer: 5 minutes

Ratio And Proportion Class 8 Questions From Real Life

Real-life ratio problems require careful comparison. Some problems look proportional but are not direct proportions.

Students should check whether both quantities increase together or one decreases when the other increases.

Q29. Kesang Uses 10 Spoons Of Sugar For 6 Glasses Of Lemonade. How Much Sugar Is Needed For 18 Glasses?

Kesang needs 30 spoons of sugar.

1. Glasses : Sugar = (6 : 10 :: 18 : x)
2. Factor from 6 to 18 = 3
3. Sugar also becomes (10 × 3)
4. (x = 30) spoons

Final Answer: 30 spoons

Q30. Nitin Builds 60 Ft Wall With 3 Cement Bags. Hari Builds 40 Ft Wall With 2 Bags. Are Both Walls Equally Strong?

Yes, both walls use cement in the same ratio.

1. Nitin’s ratio = (60 : 3 = 20 : 1)
2. Hari’s ratio = (40 : 2 = 20 : 1)
3. Both ratios are proportional.

Final Answer: Both walls are equally strong by cement ratio.

Q31. A Farmer Sells 200 g Tea For ₹200. Another Sells 1 Kg Tea For ₹800. Which Tea Is Costlier?

The Himachal tea at ₹200 for 200 g is costlier.

1. 1 kg = 1000 g
2. 200 g costs ₹200
3. 1000 g costs (₹200 × 5 = ₹1000)
4. Meghalaya tea costs ₹800 per kg.

Final Answer: Himachal tea is costlier at ₹1000 per kg.

Q32. Can 50:2::75:____ Represent Speed And Time For The Same Journey?

No, this proportion is wrong because time decreases when speed increases.

Direct proportion works when both quantities increase together. In a fixed-distance journey, higher speed gives lower time.

Example: Speed and time for a fixed distance are not directly proportional.

Sharing In A Ratio Class 8 Questions

Sharing in a ratio means dividing a whole into unequal parts. The total number of ratio units decides the size of each part.

This idea is used in money, profit, mixtures, counters, and paint.

Q33. How Do You Divide A Quantity In The Ratio m:n?

To divide (x) in the ratio (m:n), use parts (m × x/(m+n)) and (n × x/(m+n)).

The total ratio units are (m+n). Each unit equals (x/(m+n)).

Example: To divide 42 in (4:3), each unit is (42/7 = 6).

Q34. Divide ₹4,500 In The Ratio 2:3.

The two parts are ₹1,800 and ₹2,700.

1. Total amount = ₹4,500
2. Ratio = (2 : 3)
3. Total parts = (2 + 3 = 5)
4. One part = (4500 ÷ 5 = ₹900)
5. Shares = (2 × 900 = ₹1800), (3 × 900 = ₹2700)

Final Answer: ₹1,800 and ₹2,700

Q35. Prashanti Invests ₹75,000 And Bhuvan Invests ₹25,000. Share ₹4,000 Profit In The Same Ratio.

Prashanti gets ₹3,000 and Bhuvan gets ₹1,000.

1. Investment ratio = (75000 : 25000)
2. Simplest form = (3 : 1)
3. Total parts = 4
4. One part = (4000 ÷ 4 = ₹1000)
5. Shares = ₹3000 and ₹1000

Final Answer: Prashanti ₹3,000, Bhuvan ₹1,000

Q36. Acid And Water Are Mixed In The Ratio 1:5. How Much Acid And Water Are In 240 mL Solution?

The solution contains 40 mL acid and 200 mL water.

1. Total solution = 240 mL
2. Ratio = (1 : 5)
3. Total parts = 6
4. One part = (240 ÷ 6 = 40) mL
5. Acid = 40 mL, Water = (5 × 40 = 200) mL

Final Answer: 40 mL acid and 200 mL water

Q37. Blue And Yellow Paint Are Mixed In 3:5 To Make 40 mL Green Paint. Find Each Colour.

Blue paint is 15 mL and yellow paint is 25 mL.

1. Total paint = 40 mL
2. Ratio = (3 : 5)
3. Total parts = 8
4. One part = (40 ÷ 8 = 5) mL
5. Blue = (3 × 5 = 15) mL
6. Yellow = (5 × 5 = 25) mL

Final Answer: 15 mL blue and 25 mL yellow

Q38. A 40 Kg Mixture Has Sand And Cement In 3:1. How Much Cement Should Be Added To Make The Ratio 5:2?

2 kg cement should be added.

1. Original ratio = (3 : 1), total = 40 kg
2. Sand = (3/4 × 40 = 30) kg
3. Cement = (1/4 × 40 = 10) kg
4. New ratio sand : cement = (5 : 2)
5. (5 : 2 :: 30 : x), so (x = 12) kg
6. Cement to add = (12 - 10 = 2) kg

Final Answer: 2 kg cement

Unit Conversion Class 8 Maths Questions

Unit conversion is needed before comparing quantities in proportion. A wrong unit gives a wrong ratio.

The chapter includes length, area, volume, and temperature conversions.

Q39. What Are Important Unit Conversions In Class 8 Maths Chapter 7?

Important conversions include (1) litre = (1000) mL and (1) acre = (43,560) square feet.

The chapter also gives (1) metre = (3.281) feet and (1) hectare = (10,000) square metres. These conversions support real-life ratio questions.

Example: (10) litres = (10,000) mL.

Q40. Convert 25°C To Fahrenheit.

25°C is equal to 77°F.

1. Formula: Fahrenheit = (9/5 ×) Celsius + 32
2. Celsius = 25
3. Fahrenheit = (9/5 × 25 + 32)
4. Fahrenheit = (45 + 32)
5. Fahrenheit = 77

Final Answer: 77°F

Q41. A Farmer Needs 10 Tonnes Manure For 1 Acre. How Much Is Needed For 200 Ft By 500 Ft?

The farmer needs about 22.96 tonnes of manure.

1. Plot area = (200 × 500 = 100000) sq ft
2. (1) acre = (43560) sq ft
3. Plot in acres = (100000 ÷ 43560 = 2.296) acres
4. Manure per acre = 10 tonnes
5. Required manure = (2.296 × 10 = 22.96) tonnes

Final Answer: About 22.96 tonnes

Q42. One Acre Costs ₹15,00,000. Find The Cost Of 2,400 Square Feet.

The cost of 2,400 square feet is about ₹82,645.

1. (1) acre = (43,560) sq ft
2. Cost of (43,560) sq ft = ₹15,00,000
3. Cost of (2,400) sq ft = (1500000 × 2400 / 43560)
4. Cost = ₹82,644.63

Final Answer: About ₹82,645

Ganita Prakash Class 8 Chapter 7 Board Exam Pattern Questions

Board-style questions in this chapter often mix ratio, unit conversion, and real-life reasoning. Students should check whether a situation is directly proportional before solving.

Use direct proportion only when both quantities change in the same direction by the same factor.

Q43. The Earth Travels 940 Million Km In A Year. How Far Does It Travel In A Week?

The Earth travels about 18.08 million km in a week.

1. Distance in 1 year = 940 million km
2. Take 1 year = 52 weeks
3. Distance in 1 week = (940 ÷ 52) million km
4. Distance = 18.08 million km

Final Answer: About 18.08 million km

Q44. Three Buses Carry 162 People. How Many Buses Are Needed For 204 Students?

Four buses are needed for 204 students.

1. People per bus = (162 ÷ 3 = 54)
2. Required buses = (204 ÷ 54 = 3.77)
3. Number of buses must be a whole number.

Final Answer: 4 buses are needed

Q45. Delhi Has 30 Million People In 1,484 Sq Km. Mumbai Has 20 Million In 550 Sq Km. Which City Is More Crowded?

Mumbai is more crowded by population density.

1. Delhi density = (30,000,000 ÷ 1484 ≈ 20,216) people/sq km
2. Mumbai density = (20,000,000 ÷ 550 ≈ 36,364) people/sq km
3. Mumbai has more people per square kilometre.

Final Answer: Mumbai is more crowded

Class 8 Maths Important Questions Chapter-Wise