NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 (PDF) – 2026-27

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 provide clear, step-by-step answers to every exercise and in-text question from the chapter Proportional Reasoning 1 of the NCERT textbook Ganita Prakash. Prepared by subject experts as per the latest NCERT (CBSE) syllabus for 2026-27, these NCERT Solutions for Class 8 Maths help you understand each concept, write exam-ready answers, and check your own solutions. You can read them online below or download the free Class 8 Maths Chapter 7 question-answer PDF.

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1

• Class: Class 8
• Subject: Maths
• Chapter: Chapter 7 – Proportional Reasoning 1
• Textbook: Ganita Prakash (NCERT)
• Study material: NCERT Solutions – questions with answers, free PDF

These solutions answer all the exercise questions of Chapter 7 Proportional Reasoning 1 — including the in-text questions, short-answer and long-answer questions, and activities — with complete explanations so you can follow the method, not just the final answer. Read the full solutions below.

NCERT Solutions Class 8 Maths Chapter 7 Proportional Reasoning 1 View Download

NCERT Solutions for Class 8 Maths Chapter 7 PDF Download

You can read the NCERT Solutions for Class 8 Maths Chapter 7 online above, or download the complete question-answer PDF to study Proportional Reasoning 1 offline at any time.

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NCERT Solutions for Class 8 Maths Chapter 7 PDF Download Link – Click Here to Download Solutions PDF

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Questions Covered in This Chapter

These NCERT Solutions answer all 67 questions of this chapter. The questions solved are:

1. Which images look similar and which ones look different?
2. Do images B and E look like the other three images?
3. Why?
4. What makes images A, C, and D appear similar, and B and E different?
5. Can you check by what factors the width and height of image D change as compared to image A? Are the factors the same?
6. By what factor should we multiply the ratio 60 : 40 (image A) to get 90 : 60 (image D)?
7. What is the simplest form of the ratios of images B and E?
8. Example 1: Are the ratios 3 : 4 and 72 : 96 proportional?
9. What is the HCF of 72 and 96?
10. Example 2: Kesang wanted to make lemonade for a celebration. She made 6 glasses of lemonade in a vessel and added 10 spoons of sugar to the drink. Her father expected more people to join the celebration. So he asked her to make 18 more glasses of lemonade. To make the lemonade with the same sweetness, how many spoons of sugar should she add?
11. How can we find the factor of change in the ratio?
12. Example 3: Nitin and Hari were constructing a compound wall around their house. Nitin was building the longer side, 60 ft in length, and Hari was building the shorter side, 40 ft in length. Nitin used 3 bags of cement but Hari used only 2 bags of cement. Nitin was worried that the wall Hari built would not be as strong as the wall he built because she used less cement. Is Nitin correct in his thinking?
13. Example 4: In my school, there are 5 teachers and 170 students. The ratio of teachers to students in my school is 5 : 170. Count the number of teachers and students in your school. What is the ratio of teachers to students in your school? Write it below. ______ : ______ Is the teacher-to-student ratio in your school proportional to the one in my school?
14. Example 5: Measure the width and height (to the nearest cm) of the blackboard in your classroom. What is the ratio of width to height of the blackboard? ______ : ______ Can you draw a rectangle in your notebook whose width and height are proportional to the ratio of the blackboard?
15. Compare the rectangle you have drawn to those drawn by your classmates. Do they all look the same?
16. Example 6: When Neelima was 3 years old, her mother’s age was 10 times her age. What is the ratio of Neelima’s age to her mother’s age? What would be the ratio of their ages when Neelima is 12 years old? Would it remain the same?
17. Example 7: Fill in the missing numbers for the following ratios that are proportional to 14 : 21. ______ : 42 6 : ______ 2 : ______
18. What factor should we multiply 14 by to get 6? Can it be an integer? Or should it be a fraction?
19. Why is this coffee stronger?
20. Why is this coffee lighter?
21. The following table shows the different ratios in which Manjunath mixes coffee decoction with milk. Write in the last column if the coffee is stronger or lighter than the regular coffee.
22. Circle the following statements of proportion that are true. (i) 4 : 7 :: 12 : 21 (ii) 8 : 3 :: 24 : 6 (iii) 7 : 12 :: 12 : 7 (iv) 21 : 6 :: 35 : 10 (v) 12 : 18 :: 28 : 12 (vi) 24 : 8 :: 9 : 3
23. Give 3 ratios that are proportional to 4 : 9. ______ : ______ ______ : ______ ______ : ______
24. Fill in the missing numbers for these ratios that are proportional to 18 : 24. 3 : ______ 12 : ______ 20 : ______ 27 : ______
25. Look at the following rectangles. Which rectangles are similar to each other? You can verify this by measuring the width and height using a scale and comparing their ratios.
26. Look at the following rectangle. Can you draw a smaller rectangle and a bigger rectangle with the same width to height ratio in your notebooks? Compare your rectangles with your classmates’ drawings. Are all of them the same? If they are different from yours, can you think why? Are they wrong?
27. The following figure shows a small portion of a long brick wall with patterns made using coloured bricks. Each wall continues this pattern throughout the wall. What is the ratio of grey bricks to coloured bricks? Try to give the ratios in their simplest form.
28. Let us draw some human figures. Measure your friend’s body — the lengths of their head, torso, arms, and legs. Write the ratios as mentioned below— head : torso ______ : ______ torso : arms ______ : ______ torso : legs ______ : ______ Now, draw a figure with head, torso, arms, and legs with equivalent ratios as above. Does the drawing look more realistic if the ratios are proportional? Why? Why not?
29. Example 8: For the mid-day meal in a school with 120 students, the cook usually makes 15 kg of rice. On a rainy day, only 80 students came to school. How many kilograms of rice should the cook make so that the food is not wasted?
30. What is the factor of change in the first term?
31. Example 9: A car travels 90 km in 150 minutes. If it continues at the same speed, what distance will it cover in 4 hours?
32. Is this the right way to formulate the question?
33. How can you find the distance covered in 240 minutes? Discuss with your classmates and find the answer using different strategies.
34. Example 10: A small farmer in Himachal Pradesh sells each 200 g packet of tea for ₹200. A large estate in Meghalaya sells each 1 kg packet of tea for ₹800. Are the weight-to-price ratios in both places proportional?
35. Which tea is more expensive? Why?
36. Activity 1: Take your favourite dish. Find out all the ingredients and their respective quantities needed to make the dish for your family. Suppose you are celebrating a festival and you want to invite 15 guests. Find out the quantities of the ingredients required to cook the same dish for them.
37. The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week?
38. A mason is building a house in the shape shown in the diagram. He needs to construct both the outer walls and the inner wall that separates two rooms. To build a wall of 10-feet, he requires approximately 1450 bricks. How many bricks would he need to build the house? Assume all walls are of the same height and thickness.
39. Puneeth’s father went from Lucknow to Kanpur in 2 hours by riding his motorcycle at a speed of 50 km/h. If he drives at 75 km/h, how long will it take him to reach Kanpur? Can we form this problem as a proportion — 50 : 2 :: 75 : __ Would it take Puneeth’s father more time or less time to reach Kanpur? Think about it.
40. Activity 2: Go to the market and collect the prices of different sizes of shampoo containers of the same shampoo and create a table like the one given below. See if the volume of shampoo is proportional to the price. (Sachet 6 mL ₹2; Small Bottle 180 mL ₹154; Medium Bottle 340 mL ₹276; Large Bottle 1000 mL ₹540)
41. The ratio of the volume of a sachet to a small bottle is 6 : 180. The ratio of their prices is 2 : 154. Are these ratios proportional?
42. Why do you think that the ratio of the prices is not proportional to the ratio of the volumes? Discuss the pros and cons of different size bottles for the company and for customers. For reducing ecological footprint, what would you recommend to the company and to the customer? Does the same occur for other products?
43. Activity 3: Form a pair. Collect 12 countable objects or counters (it can be coins, seeds, or pebbles). Now, share them between the two of you in different ways. If you divide them equally, what is the ratio of the number of counters with each of you?
44. If your partner gets 5 counters, how many objects will you get? What is the ratio of the counters?
45. Now, if you want to share the counters between the two of you in the ratio of 3 : 1, how many counters would each of you get?
46. Now, if you want to share 42 counters between the two of you in the ratio of 4 : 3, how will you do it?
47. What is the size of each group?
48. Divide ₹4,500 into two parts in the ratio 2 : 3.
49. In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain?
50. Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of these two colours are needed? To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint?
51. To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need?
52. I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. I added another bucket of yellow paint to this mixture. What is the ratio of red paint to yellow paint in the new mixture?
53. Anagh mixes 600 mL of orange juice with 900 mL of apple juice to make a fruit drink. Write the ratio of orange juice to apple juice in its simplest form.
54. Last year, we hired 3 buses for the school trip. We had a total of 162 students and teachers who went on that trip and all the buses were full. This year we have 204 students. How many buses will we need? Will all the buses be full?
55. The area of Delhi is 1,484 sq. km and the area of Mumbai is 550 sq. km. The population of Delhi is approximately 30 million and that of Mumbai is 20 million people. Which city is more crowded? Why do you say so?
56. A crane of height 155 cm has its neck and the rest of its body in the ratio 4 : 6. For your height, if your neck and the rest of the body also had this ratio, how tall would your neck be?
57. Let us try an ancient problem from Lilavati. At that time weights were measured in a unit named palas and niskas was a unit of money. “If 2½ palas of saffron costs 3⁄7 niskas, O expert businessman! tell me quickly what quantity of saffron can be bought for 9 niskas?”
58. Harmain is a 1-year-old girl. Her elder brother is 5 years old. What will be Harmain’s age when the ratio of her age to her brother’s age is 1 : 2?
59. The mass of equal volumes of gold and water are in the ratio 37 : 2. If 1 litre of water is 1 kg in mass, what is the mass of 1 litre of gold?
60. It is good farming practice to apply 10 tonnes of cow manure for 1 acre of land. A farmer is planning to grow tomatoes in a plot of size 200 ft by 500 ft. How much manure should he buy? (Please refer to the section on Unit Conversions earlier in this chapter).
61. A tap takes 15 seconds to fill a mug of water. The volume of the mug is 500 mL. How much time does the same tap take to fill a bucket of water if the bucket has a 10-litre capacity?
62. One acre of land costs ₹15,00,000. What is the cost of 2,400 square feet of the same land?
63. A tractor can plough the same area of a field 4 times faster than a pair of oxen. A farmer wants to plough his 20-acre field. A pair of oxen takes 6 hours to plough an acre of land. How much time would it take if the farmer used a pair of oxen to plough the field? How much time would it take him if he decides to use a tractor instead?
64. The ₹10 coin is an alloy of copper and nickel called ‘cupro-nickel’. Copper and nickel are mixed in a 3 : 1 ratio to get this alloy. The mass of the coin is 7.74 grams. If the cost of copper is ₹906 per kg and the cost of nickel is ₹1,341 per kg, what is the cost of these metals in a ₹10 coin?
65. Solve the following Binairo puzzles: (first grid — a vertical line in row 2 column 3; horizontal lines in row 2 columns 5 and 6; a horizontal line in row 3 column 2; vertical lines in row 4 columns 3 and 5; horizontal lines in row 5 columns 1 and 5; a vertical line in row 6 column 3)
66. Solve the following Binairo puzzles: (second grid — horizontal lines in row 1 column 1, row 2 columns 1 and 6, row 5 column 6; vertical lines in row 3 column 4, row 4 columns 2 and 3, row 6 columns 2 and 5)
67. Solve the following Binairo puzzles: (third grid — a horizontal line in row 1 column 5, row 2 column 6, row 3 columns 1, 3 and 6; vertical lines in row 5 columns 3 and 4, and row 6 column 1)

Chapter at a Glance

• Two figures look alike when their measurements change by the same factor (multiplication). Changing both by the same amount (subtraction) distorts them — that is exactly why image B, made by taking 20 mm off both sides of A, looks elongated.
• A ratio a : b says that for every a units of the first quantity there are b units of the second. Dividing both terms by their HCF puts the ratio in its simplest form, which is the fingerprint used to compare ratios.
• Two ratios are in proportion, written a : b :: c : d, when their simplest forms agree. Algebraically this is the same as ad = bc — the cross multiplication rule, which the chapter derives rather than states.
• Trairasika, the Rule of Three: given three of the four terms, the fourth is d = bc⁄a. Āryabhaṭa put it as ichchhāphala = (phala × ichchhā) ÷ pramāṇa.
• To divide a quantity x in the ratio m : n, cut x into m + n equal groups; the two parts are m × x⁄(m+n) and n × x⁄(m+n).
• Not every problem with four numbers is a proportion. When speed rises the time for a fixed journey falls, so 50 : 2 :: 75 : __ is the wrong model. And terms can only be compared after the units are made to match — 4 hours must become 240 minutes, 1 kg must become 1000 g.

How to Download NCERT Solutions for Class 8 Maths Chapter 7 PDF

Follow these simple steps to get the Proportional Reasoning 1 questions-and-answers PDF from Ganita Prakash.

1. Search NCERT Solutions for Class 8 Maths Chapter 7 aglasem and open this page.
2. Read the exercise questions with answers for Proportional Reasoning 1 shown above.
3. Click the Download PDF link to save the Proportional Reasoning 1 solutions to your device.

NCERT Solutions for Class 8 Maths – All Chapters

There are more chapters to study besides Proportional Reasoning 1 in Maths. Here are the NCERT Solutions for all chapters of Class 8 Maths.

• Chapter 1 A Square and a Cube
• Chapter 2 Power Play
• Chapter 3 A Story of Numbers
• Chapter 4 Quadrilaterals
• Chapter 5 Number Play
• Chapter 6 We Distribute Yet Things Multiply
• Chapter 7 Proportional Reasoning 1
• Chapter 8 Fractions in Disguise
• Chapter 9 The Baudh Yana Pythagoras Theorem
• Chapter 10 Proportional Reasoning 2
• Chapter 11 Exploring Some Geometric Themes
• Chapter 12 Tales By Dots and Lines
• Chapter 13 Algebra Play
• Chapter 14 Area

NCERT Solutions for Class 8 – All Subjects

Just like Chapter 7 of Maths, you can get the exercise questions with answers for every other subject of Class 8. Here are the NCERT Solutions for all subjects of Class 8.

• English
• Hindi
• Maths
• Sanskrit
• Science
• Social Science

NCERT Solutions for Class 8 Maths Chapter 7 – An Overview

The key highlights of this study material are as follows.

Aspects	Details
Class	Class 8
Subject	Maths
Chapter Number	Chapter 7
Chapter Name	Proportional Reasoning 1
Book Name	Ganita Prakash
Book By	NCERT (National Council of Educational Research and Training)
Educational Resource Here	NCERT Solutions of Class 8 Maths Chapter 7 for all exercises
More Questions Answers of This Subject	NCERT Solutions for Class 8 Maths
Download Book Chapter	NCERT Book Class 8 Maths
All Questions Answers For This Class	NCERT Solutions for Class 8
Complete Solutions	NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 – FAQs

What are the NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1?

They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 7 Proportional Reasoning 1 from the NCERT Class 8 Maths textbook Ganita Prakash, written by experts as per the latest NCERT syllabus.

How can I download the Class 8 Maths Chapter 7 solutions PDF for free?

Open this page on aglasem, read the Proportional Reasoning 1 questions with answers, and click the “Download Solutions PDF” link. The Class 8 Maths Chapter 7 NCERT Solutions PDF is completely free to download.

Are these NCERT Solutions as per the latest 2026-27 syllabus?

Yes. The NCERT Solutions for Class 8 Maths Chapter 7 are based on the latest NCERT textbook Ganita Prakash and the current 2026-27 CBSE syllabus, so the questions and answers match what you study in class.

Where can I get NCERT Solutions for the other chapters of Class 8 Maths?

You can find the answers to every chapter on the NCERT Solutions for Class 8 Maths page, and solutions for every subject on the NCERT Solutions for Class 8 page.

How do NCERT Solutions help in exam preparation?

They show the correct method to solve each question, help you write answers the way they are expected in exams, let you check and correct your own work, and save revision time — which together improve your marks in Class 8 Maths.

If you have any queries on NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1, then please ask in the comments below.