Class 8 Maths Chapter 3 Proportional Reasoning-2

Proportional reasoning is one of the most useful skills in Class 8 Maths, connecting ratios, fractions, and real-life situations. This chapter builds on earlier ideas and shows how quantities change in relation to one another. Students learn to recognise when two quantities are in direct proportion (both increase or decrease together) and when they are in inverse proportion (one increases as the other decreases). Mastering this chapter makes topics like speed, percentage, scale drawing, and everyday calculations much easier.

In direct proportion, the ratio of two quantities stays constant: a/b = constant. In inverse proportion, the product of two quantities stays constant: a × b = constant. The unitary method — finding the value of one unit first — is the most reliable tool for solving these problems.

Class 8 Maths Chapter 3 Proportional Reasoning-2

Q1. If 12 pens cost Rs. 96, find the cost of 7 pens.

This is a case of direct proportion — more pens cost more money. We use the unitary method.

  • Cost of 1 pen = 96 ÷ 12 = Rs. 8
  • Cost of 7 pens = 8 × 7 = Rs. 56

Conclusion: The cost of 7 pens is Rs. 56.

Q2. A car travels 240 km using 16 litres of petrol. How much petrol is needed to travel 360 km?

Distance and petrol are in direct proportion. Find petrol per km first.

  • Petrol for 1 km = 16 ÷ 240 = 1/15 litre
  • Petrol for 360 km = (1/15) × 360 = 24 litres

Conclusion: 24 litres of petrol are needed to travel 360 km.

Q3. 15 workers can build a wall in 8 days. How many days will 10 workers take to build the same wall?

More workers means fewer days, so this is inverse proportion. The product (workers × days) stays constant.

  • Total work = 15 × 8 = 120 worker-days
  • Days for 10 workers = 120 ÷ 10 = 12 days

Conclusion: 10 workers will take 12 days to build the wall.

Q4. The ratio of boys to girls in a class is 5 : 3. If there are 40 boys, how many girls are there?

Set up equivalent ratios. Boys : Girls = 5 : 3.

  • 5 parts = 40 boys, so 1 part = 40 ÷ 5 = 8
  • Girls = 3 parts = 3 × 8 = 24

Conclusion: There are 24 girls in the class.

Q5. A map uses a scale of 1 cm = 50 km. If two cities are 7.5 cm apart on the map, find the actual distance.

Map distance and actual distance are in direct proportion based on the scale.

  • 1 cm represents 50 km
  • Actual distance = 7.5 × 50 = 375 km

Conclusion: The actual distance between the two cities is 375 km.

Q6. If 6 taps fill a tank in 80 minutes, how long will 5 taps take to fill the same tank?

Fewer taps means more time, so this is inverse proportion.

  • Total work = 6 × 80 = 480 tap-minutes
  • Time for 5 taps = 480 ÷ 5 = 96 minutes

Conclusion: 5 taps will take 96 minutes to fill the tank.

Q7. The cost of 5 kg of sugar is Rs. 225. Find the cost of 8 kg of sugar.

Weight and cost are in direct proportion. Use the unitary method.

  • Cost of 1 kg = 225 ÷ 5 = Rs. 45
  • Cost of 8 kg = 45 × 8 = Rs. 360

Conclusion: The cost of 8 kg of sugar is Rs. 360.

Q8. Two numbers are in the ratio 4 : 7 and their sum is 88. Find the two numbers.

Express both numbers in terms of one common part.

  • Let the numbers be 4x and 7x. Then 4x + 7x = 88
  • 11x = 88, so x = 8
  • Numbers = 4 × 8 = 32 and 7 × 8 = 56

Conclusion: The two numbers are 32 and 56.

Q9. A garrison of 120 soldiers has food for 30 days. If 30 more soldiers join, how long will the food last?

More soldiers means food lasts fewer days — inverse proportion.

  • Total food = 120 × 30 = 3600 soldier-days
  • New number of soldiers = 120 + 30 = 150
  • Days = 3600 ÷ 150 = 24 days

Conclusion: The food will last 24 days.

Q10. A recipe for 4 people needs 600 g of flour. How much flour is needed for 10 people?

Number of people and flour are in direct proportion.

  • Flour for 1 person = 600 ÷ 4 = 150 g
  • Flour for 10 people = 150 × 10 = 1500 g (1.5 kg)

Conclusion: 1500 g (1.5 kg) of flour is needed for 10 people.

Frequently Asked Questions (FAQs)

1. What types of important questions are asked from this chapter in school exams? Class 8 exams feature MCQs, short-answer ratio questions, and word problems based on direct and inverse proportion — covering cost, speed, work-and-time, scale drawings, and sharing in a given ratio.

2. How should I write answers for this chapter to score full marks? First identify whether it is direct or inverse proportion. Write the relationship clearly, show the unitary method step by step, and always write the correct units (Rs., km, kg, days) in the final answer.

3. What are the highest-weightage subtopics in this chapter? The most important topics are direct proportion, inverse proportion, the unitary method, and dividing a quantity in a given ratio. Word problems on work-and-time and speed-distance carry good marks.

4. How do I quickly decide between direct and inverse proportion? Ask: "If one quantity increases, does the other increase or decrease?" If both move the same way (more pens → more cost), it is direct. If they move opposite ways (more workers → fewer days), it is inverse.

5. How can I quickly revise this chapter before a test? Review all solved important questions, memorise the two key rules (a/b = constant for direct, a×b = constant for inverse), practise a few word problems of each type, and keep your steps neat for full step marks.

6. Do I get step marks if my final calculation is wrong? Yes. CBSE and most boards follow step marking. You earn partial marks for correctly identifying the type of proportion, writing the right setup, and substituting values correctly — even if the final arithmetic has an error.