Important Questions Class 8 Maths Part 2 Chapter 3 Proportional Reasoning-2

Proportional reasoning compares quantities through ratios, fractions, scales, and constant relationships. Important Questions Class 8 Maths Part 2 Chapter 3 cover Proportional Reasoning-2, including ratios in maps, Representative Fraction, multi-term ratios, dividing in a given ratio, pie charts, inverse proportion, and word problems.

A recipe, a map, a pie chart, and a team of workers all use proportional reasoning in different ways.

Class 8 Maths Chapter 3 Proportional Reasoning-2 teaches students to read ratios beyond simple comparisons. The chapter becomes easier when students first decide whether quantities grow together, split a whole, represent a scale, or move in opposite directions like workers and time.

Key Takeaways

Class 8 Maths Part 2 Chapter List

Important Topics in Class 8 Maths Chapter 3 Proportional Reasoning-2

Important questions for class 8 maths chapter 3 mostly come from ratios, maps, pie charts, and inverse proportion.

Do not treat every question as direct proportion. First check what changes and what stays constant.

Important Questions Class 8 Maths Part 2 Chapter 3 with Answers

Important Questions Class 8 Maths Part 2 Chapter 3 should be practised topic-wise. Start with map scales and ratios, then move to pie charts and inverse proportion.

These proportional reasoning 2 class 8 questions and answers help students practise calculations, reasoning, and real-life word problems together.

Ratios in Maps Class 8 Questions

Ratios in maps class 8 questions use Representative Fraction to connect map distance with real ground distance.

RF has no unit because both distances are written in the same unit.

Representative Fraction Class 8 Questions

Q1. What does RF 1 : 60,00,000 mean on a map?
Ans. RF stands for Representative Fraction.

A scale of 1 : 60,00,000 means 1 unit on the map represents 60,00,000 of the same units on the ground.

So,

1 cm on the map = 60,00,000 cm on the ground

60,00,000 cm = 60 km

Q2. Convert 60,00,000 cm to kilometres.
Ans.

60,00,000 cm ÷ 100 = 60,000 m

60,000 m ÷ 1000 = 60 km

So,

60,00,000 cm = 60 km

Q3. On a map with scale 1 : 60,00,000, the distance between Bengaluru and Chennai is 2.5 cm. Find the actual distance.
Ans.

Actual distance = Map distance × Scale factor

= 2.5 × 60,00,000 cm

= 1,50,00,000 cm

Now convert to km:

1,50,00,000 cm ÷ 100 = 1,50,000 m

1,50,000 m ÷ 1000 = 150 km

Actual distance = 150 km

Q4. A map has RF 1 : 50,00,000. What actual distance is represented by 3 cm on the map?
Ans.

1 cm = 50,00,000 cm

3 cm = 3 × 50,00,000 cm

= 1,50,00,000 cm

= 150 km

Actual distance = 150 km

Multi-Term Ratio Class 8 Questions

Multi term ratio class 8 questions involve three or more quantities.

Find the value of one part first. Then multiply it by each ratio term.

Ratio Class 8 Maths Questions

Q1. To make purple paint, Red : Blue : White = 2 : 3 : 5. Yasmin has 10 litres of white paint. How many litres of red and blue should she add?
Ans.

White = 5 parts = 10 litres

So,

1 part = 10 ÷ 5

= 2 litres

Red = 2 parts

= 2 × 2

= 4 litres

Blue = 3 parts

= 3 × 2

= 6 litres

Total purple paint = 4 + 6 + 10

= 20 litres

Q2. Cement concrete is mixed in the ratio Cement : Sand : Gravel = 1 : 1.5 : 3. If 3 bags of cement are used, how many bags of sand and gravel are needed?
Ans.

Cement = 1 part = 3 bags

So,

1 part = 3 bags

Sand = 1.5 parts

= 1.5 × 3

= 4.5 bags

Gravel = 3 parts

= 3 × 3

= 9 bags

Total mixture = 3 + 4.5 + 9

= 16.5 bags

Q3. A school library has Odiya : Hindi : English books in the ratio 3 : 2 : 1. If the library has 288 Odiya books, how many Hindi and English books does it have?
Ans.

Odiya = 3 parts = 288

1 part = 288 ÷ 3

= 96

Hindi = 2 × 96

= 192 books

English = 1 × 96

= 96 books

Q4. A cricket coach schedules sessions with Warm-up : Batting : Bowling : Fielding = 3 : 4 : 3 : 5. Each session is 150 minutes. How much time is spent on each activity?
Ans.

Total parts = 3 + 4 + 3 + 5

= 15

Each part = 150 ÷ 15

= 10 minutes

Warm-up = 3 × 10 = 30 minutes

Batting = 4 × 10 = 40 minutes

Bowling = 3 × 10 = 30 minutes

Fielding = 5 × 10 = 50 minutes

Dividing in a Given Ratio Class 8 Questions

Dividing in a given ratio class 8 questions ask students to split one total into parts.

Add all ratio terms first. Then multiply each fraction by the total.

Ganita Prakash Class 8 Part 2 Chapter 3 Questions

Q1. 110 units of concrete are needed. How many units of cement, sand, and gravel are needed if mixed in the ratio 1 : 1.5 : 3?
Ans.

Total parts = 1 + 1.5 + 3

= 5.5

Cement = 1/5.5 × 110

= 20 units

Sand = 1.5/5.5 × 110

= 30 units

Gravel = 3/5.5 × 110

= 60 units

Check:

20 + 30 + 60 = 110

Q2. 50 ml of purple paint is needed using Red : Blue : White = 2 : 3 : 5. Find the amount of each colour.
Ans.

Total parts = 2 + 3 + 5

= 10

Red = 2/10 × 50

= 10 ml

Blue = 3/10 × 50

= 15 ml

White = 5/10 × 50

= 25 ml

Q3. I have 100 coins in the ratio ₹10 : ₹5 : ₹2 : ₹1 = 4 : 3 : 2 : 1. How much money do I have?
Ans.

Total parts = 4 + 3 + 2 + 1

= 10

Each part = 100 ÷ 10

= 10 coins

₹10 coins = 4 × 10 = 40 coins

Value = 40 × 10 = ₹400

₹5 coins = 3 × 10 = 30 coins

Value = 30 × 5 = ₹150

₹2 coins = 2 × 10 = 20 coins

Value = 20 × 2 = ₹40

₹1 coins = 1 × 10 = 10 coins

Value = 10 × 1 = ₹10

Total value = 400 + 150 + 40 + 10

= ₹600

Q4. Construct a triangle with angles in the ratio 1 : 3 : 5. Find the angles.
Ans.

Total parts = 1 + 3 + 5

= 9

Sum of angles in a triangle = 180°

Each part = 180 ÷ 9

= 20°

Angles:

1 × 20 = 20°

3 × 20 = 60°

5 × 20 = 100°

So, the angles are 20°, 60°, and 100°.

Q5. Can you construct a triangle with side lengths in the ratio 1 : 3 : 5? Why?
Ans. No, such a triangle cannot be constructed.

For any triangle, the sum of any two sides must be greater than the third side.

Here,

1 + 3 = 4

4 is less than 5.

So, the triangle inequality is not satisfied.

Pie Chart Class 8 Maths Questions

Pie chart class 8 maths questions convert data into sector angles.

Use this formula:

Angle = Value/Total × 360°

Pie Chart Questions with Answers

Q1. 360 people voted for favourite seasons: Summer = 90, Rainy = 120, Winter = 150. Find the angle for each pie chart sector.
Ans.

Total = 360 people

Summer angle = 90/360 × 360°

= 90°

Rainy angle = 120/360 × 360°

= 120°

Winter angle = 150/360 × 360°

= 150°

Check:

90° + 120° + 150° = 360°

Q2. A pie chart shows viewers’ favourite TV channels: Entertainment = 50%, Sports = 25%, News = 15%, Information = 10%. Find the angle for each sector.
Ans.

Angle = Percentage/100 × 360°

Entertainment = 50/100 × 360°

= 180°

Sports = 25/100 × 360°

= 90°

News = 15/100 × 360°

= 54°

Information = 10/100 × 360°

= 36°

Check:

180° + 90° + 54° + 36° = 360°

Q3. A pie chart shows modes of transport to school: Walk = 90°, Bus = 120°, Cycle = 60°, Two-wheeler = 60°, Car = 30°. Which is the most common mode? What fraction travel by car? If 18 children travel by car, how many children took part in the survey?
Ans.

Largest angle = 120°

So, bus is the most common mode.

Car sector = 30°

Fraction travelling by car = 30/360

= 1/12

If 1/12 of total = 18,

Total = 18 × 12

= 216 children

Inverse Proportion Class 8 Questions

Inverse proportion class 8 questions are the highest-weightage part of this chapter.

When one quantity increases and the other decreases so that their product stays constant, the quantities are in inverse proportion.

Inverse Proportion Class 8 Questions with Answers

Q1. Which of these are in inverse proportion?

(i) x: 40, 80, 25, 16; y: 20, 10, 32, 50
(ii) x: 40, 80, 25, 16; y: 20, 10, 12.5, 8
(iii) x: 30, 90, 150, 10; y: 15, 5, 3, 45

Ans.

For inverse proportion, xy must be constant.

(i)

40 × 20 = 800
80 × 10 = 800
25 × 32 = 800
16 × 50 = 800

All products are equal.

So, (i) is inverse proportion.

(ii)

40 × 20 = 800
80 × 10 = 800
25 × 12.5 = 312.5
16 × 8 = 128

Products are not equal.

So, (ii) is not inverse proportion.

(iii)

30 × 15 = 450
90 × 5 = 450
150 × 3 = 450
10 × 45 = 450

All products are equal.

So, (iii) is inverse proportion.

Q2. Fill in the empty cells if x and y are in inverse proportion: x: 16, 12, __, 36 and y: 9, __, 48, __.
Ans.

Since x and y are in inverse proportion:

xy = constant

Using x = 16 and y = 9:

k = 16 × 9

= 144

When x = 12:

y = 144 ÷ 12

= 12

When y = 48:

x = 144 ÷ 48

= 3

When x = 36:

y = 144 ÷ 36

= 4

Complete table:

Q3. 20 workers take 4 days to complete laying a road. How many days will 10 workers take?
Ans.

Workers × Days = constant

20 × 4 = 80

For 10 workers:

10 × Days = 80

Days = 80 ÷ 10

= 8 days

Q4. 2 pumps fill a tank in 18 hours. How long will it take if 2 more pumps of the same kind are added?
Ans.

Total pumps after adding 2 pumps = 4

Pumps × Time = constant

2 × 18 = 36

For 4 pumps:

4 × Time = 36

Time = 36 ÷ 4

= 9 hours

Q5. A school has food provisions for 80 students for 15 days. If 20 more students join, how many days will the provisions last?
Ans.

Students × Days = constant

80 × 15 = 1200

New number of students = 80 + 20

= 100

Days = 1200 ÷ 100

= 12 days

The provisions will last for 12 days.

Q6. Ram takes 1 hour and Shyam takes 1.5 hours to cut the same quantity of vegetables. How long will they take together?
Ans.

Ram’s rate = 1 work per hour

Shyam’s rate = 1/1.5

= 2/3 work per hour

Combined rate = 1 + 2/3

= 5/3 work per hour

Time = 1 ÷ 5/3

= 3/5 hour

= 36 minutes

Q7. Three workers paint a fence in 4 days. If one more worker joins, how many days will it take?
Ans.

Workers × Days = constant

3 × 4 = 12

New workers = 4

Days = 12 ÷ 4

= 3 days

Q8. A car travels at 60 km/h and takes 2 hours to reach a destination. How long will it take at 80 km/h?
Ans.

Distance = Speed × Time

Distance = 60 × 2

= 120 km

At 80 km/h:

Time = 120 ÷ 80

= 1.5 hours

Q9. 24 pencils cost ₹120. How much will 20 pencils cost?
Ans.

This is direct proportion.

Cost per pencil = 120 ÷ 24

= ₹5

Cost of 20 pencils = 20 × 5

= ₹100

Q10. A factory needs 42 machines to produce toys in 63 days. How many machines are needed to produce the same toys in 54 days?
Ans.

Machines × Days = constant

42 × 63 = 2646

For 54 days:

Machines = 2646 ÷ 54

= 49

So, 49 machines are needed.

Q11. A small pump fills a tank in 3 hours. A large pump fills the same tank in 2 hours. How long will they take together?
Ans.

Small pump rate = 1/3 tank per hour

Large pump rate = 1/2 tank per hour

Combined rate = 1/3 + 1/2

= 2/6 + 3/6

= 5/6 tank per hour

Time = 1 ÷ 5/6

= 6/5 hours

= 1 hour 12 minutes

Q12. A school has 8 periods of 45 minutes each. If rearranged to 9 periods, how long is each period?
Ans.

Total time = 8 × 45

= 360 minutes

With 9 periods:

Each period = 360 ÷ 9

= 40 minutes

Q13. Which of the following pairs are in inverse proportion?

(i) Number of taps filling a tank and time taken
(ii) Number of painters and days to paint a fixed wall
(iii) Distance a car travels and petrol in the tank
(iv) Speed of a cyclist and time to cover a fixed route
(v) Length of cloth bought and price paid at fixed rate
(vi) Pages in a book and time to read at fixed speed

Ans.

(i) Inverse proportion

(ii) Inverse proportion

(iii) Direct proportion

(iv) Inverse proportion

(v) Direct proportion

(vi) Direct proportion

Direct and Inverse Proportion Class 8 Questions

Direct and inverse proportion class 8 questions ask students to identify the relationship before solving.

In direct proportion, both quantities increase or decrease together. In inverse proportion, one increases while the other decreases.

Maths Questions for Class 8 with Answers

Q1. How can you identify direct proportion?
Ans. In direct proportion, the ratio of two quantities remains constant.

If one quantity doubles, the other also doubles.

Example: More pencils cost more money at the same rate.

Q2. How can you identify inverse proportion?
Ans. In inverse proportion, the product of two quantities remains constant.

If one quantity doubles, the other becomes half.

Example: More workers take fewer days to complete the same work.

Q3. Is the relation between speed and time direct or inverse for a fixed distance?
Ans. It is inverse proportion.

For a fixed distance:

Speed × Time = Distance

If speed increases, time decreases.

Q4. Is the relation between quantity bought and cost direct or inverse at a fixed rate?
Ans. It is direct proportion.

If the quantity increases, the cost increases in the same ratio.

Important MCQs for Class 8 Maths Chapter 3

MCQs from this chapter usually test formula selection and relationship identification.

Read whether the question asks for direct or inverse change.

Q1. In inverse proportion, if x doubles, y:
(a) Doubles
(b) Halves
(c) Stays the same
(d) Quadruples

Ans. (b) Halves

In inverse proportion, xy = constant.

Q2. RF 1 : 50,00,000 means 1 cm on map equals:
(a) 5 km
(b) 50 km
(c) 500 km
(d) 5000 km

Ans. (b) 50 km

50,00,000 cm = 50 km

Q3. Paint is mixed in the ratio R : B : W = 2 : 3 : 5. In 40 litres of purple paint, white paint used is:
(a) 8 litres
(b) 12 litres
(c) 20 litres
(d) 16 litres

Ans. (c) 20 litres

White = 5/10 × 40

= 20 litres

Q4. Triangles with side lengths in the ratio 3 : 4 : 5 are:
(a) Congruent
(b) Similar but not necessarily congruent
(c) Neither similar nor congruent
(d) Always equilateral

Ans. (b) Similar but not necessarily congruent

Same ratio fixes shape, not size.

Q5. A pie chart sector for 90 people out of 360 has central angle:
(a) 90°
(b) 45°
(c) 120°
(d) 270°

Ans. (a) 90°

Angle = 90/360 × 360°

= 90°

Q6. In the equation xy = k, if x = 6 and k = 48, then y is:
(a) 6
(b) 8
(c) 48
(d) 288

Ans. (b) 8

y = 48 ÷ 6

= 8

HOTS and Application Questions from Class 8 Maths Chapter 3

HOTS questions test whether students can identify the relationship correctly.

Do not assume every word problem is inverse proportion.

Class 8 Maths Extra Questions Chapter 3

Q1. A tank has water for 20 families for 6 days. If 10 more families move in, how long will the water last?
Ans.

Families × Days = constant

20 × 6 = 120

New families = 20 + 10

= 30

Days = 120 ÷ 30

= 4 days

Q2. One pump takes 6 hours to fill 2 tanks of the same size. How long will it take to fill 5 such tanks?
Ans.

Time for 1 tank = 6 ÷ 2

= 3 hours

Time for 5 tanks = 5 × 3

= 15 hours

This is direct proportion.

More tanks need more time with the same pump.

Q3. 25 rows have 12 chairs each. If rearranged with 20 chairs per row, how many rows are needed?
Ans.

Total chairs = 25 × 12

= 300

New rows = 300 ÷ 20

= 15 rows

Q4. Viswanath mixes 6 cups rice and 3 cups urad dal. Puneet mixes 4 cups rice and 2 cups urad dal. Will their idlis taste the same?
Ans.

Viswanath’s ratio = 6 : 3

= 2 : 1

Puneet’s ratio = 4 : 2

= 2 : 1

Both ratios are equal.

So, their idlis will taste the same.

Ganita Prakash Class 8 Part 2 Solutions: Chapter 3 Practice

Ganita Prakash Class 8 Part 2 solutions for this chapter focus on real situations.

Students should not only calculate the answer but also explain why the relation is direct, inverse, or ratio-based.

Proportional Reasoning 2 Class 8 Solutions Practice

Q1. Why does inverse proportion apply to workers and days?
Ans. For a fixed amount of work, more workers complete the work in fewer days.

The product Workers × Days stays constant.

So, workers and days are in inverse proportion.

Q2. Why is cost of pencils direct proportion, not inverse proportion?
Ans. If each pencil has the same price, more pencils cost more money.

The ratio Cost/Number of pencils stays constant.

So, pencil number and cost are in direct proportion.

Q3. Why is RF called Representative Fraction?
Ans. RF represents the fraction:

Map distance / Actual distance

Both distances are written in the same unit.

That is why RF has no unit.

Key Formulas and Concepts from Class 8 Maths Chapter 3