NCERT Solutions for Class 8 Maths Chapter 10 Proportional Reasoning 2 provide clear, step-by-step answers to every exercise and in-text question from the chapter Proportional Reasoning 2 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 10 question-answer PDF.
NCERT Solutions for Class 8 Maths Chapter 10 Proportional Reasoning 2
- Class: Class 8
- Subject: Maths
- Chapter: Chapter 10 – Proportional Reasoning 2
- Textbook: Ganita Prakash (NCERT)
- Study material: NCERT Solutions – questions with answers, free PDF
These solutions answer all the exercise questions of Chapter 10 Proportional Reasoning 2 — 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 10 Proportional Reasoning 2 View Download
NCERT Solutions for Class 8 Maths Chapter 10 PDF Download
You can read the NCERT Solutions for Class 8 Maths Chapter 10 online above, or download the complete question-answer PDF to study Proportional Reasoning 2 offline at any time.
NCERT Solutions for Class 8 Maths Chapter 10 PDF Download Link – Click Here to Download Solutions PDF
Questions Covered in This Chapter
These NCERT Solutions answer all 37 questions of this chapter. The questions solved are:
- Viswanath made idlis by mixing 6 cups of rice with 3 cups of urad dal, while Puneet made idlis by mixing 4 cups of rice with 2 cups of urad dal. If cooked in the same way, would their idlis taste the same?
- Have you noticed that in many maps there is a ratio given, usually in the lower right corner of the map? It usually contains 1 and a very large number, such as 1 : 60,00,000. What does RF 1 : 60,00,000 mean? What does it indicate? Can you guess?
- Convert 60,00,000 cm to kilometres. (It is 60 km. Verify this.)
- Using the map above, can you find the geographical distance between Bengaluru and Chennai? Also, find the geographical distance between Mangaluru and Chennai. [Hint: Use a ruler to find the distance between the cities on the map. Then, use the ratio given on the map to find the actual geographical distance.]
- Try to find the distances between the same two pairs of cities with different maps that have different scales (ratios). Do they all give the same geographical distance, approximately?
- Map Making Activity: Guide students to make a sketch of their classroom with an accurate scale (ratio of 1 : 50). They should mark the location of various objects in the classroom like the teacher’s desk, blackboard, fans and lights, according to scale. Students can use appropriate symbols to represent different objects like fans, lights, tables, chairs, and so on.
- Puneet has only 2 red chillies in his kitchen. But he wants to make spice mix powder that tastes the same as Viswanath’s spice mix powder. How much of the other ingredients should Puneet use to make his spice mix powder?
- What is the total volume of this purple paint? (Red : Blue : White :: 2 : 3 : 5, with 4 litres of red, 6 litres of blue and 10 litres of white.)
- A cricket coach schedules practice sessions that include different activities in a specific ratio — time for warm-up/cool-down : time for batting : time for bowling : time for fielding :: 3 : 4 : 3 : 5. If each session is 150 minutes long, how much time is spent on each activity?
- A school library has books in different languages in the following ratio — no. of Odiya books : no. of Hindi books : no. of English books :: 3 : 2 : 1. If the library has 288 Odiya books, how many Hindi and English books does it have?
- I have 100 coins in the ratio — no. of ₹10 coins : no. of ₹5 coins : no. of ₹2 coins : no. of ₹1 coins :: 4 : 3 : 2 : 1. How much money do I have in coins?
- Construct a triangle with sidelengths in the ratio 3 : 4 : 5. Will all the triangles drawn with this ratio of sidelengths be congruent to each other? Why or why not?
- Can you construct a triangle with sidelengths in the ratio 1 : 3 : 5? Why or why not?
- How do we mark the different slices of the pie chart?
- Can we reduce this ratio to its simplest form?
- A group of 360 people were asked to vote for their favourite season from the three seasons — rainy, winter and summer. 90 liked the summer season, 120 liked the rainy season, and the rest liked the winter. Draw a pie chart to show this information.
- Draw a pie chart based on the following information about viewers’ favourite type of TV channel: Entertainment — 50%, Sports — 25%, News — 15%, Information — 10%.
- Prepare a pie chart that shows the favourite subjects of the students in your class. You can collect the data of the number of students for each subject shown in the table (each student should choose only one subject). Then write these numbers in the table and construct a pie chart. (Subjects: Language, Arts Education, Vocational Education, Social Science, Physical Education, Maths, Science)
- Can we represent this problem with the following statement of proportionality — 30 : 60 :: 3 : x ? Will the travel time increase or decrease as the speed of the motorcycle increases?
- Does it decrease by the same rate (or factor)?
- Check if this is the case for the other modes of transport.
- Which of these are in inverse proportion? (i) x: 40, 80, 25, 16 and y: 20, 10, 32, 50. (ii) x: 40, 80, 25, 16 and y: 20, 10, 12.5, 8. (iii) x: 30, 90, 150, 10 and y: 15, 5, 3, 45.
- Fill in the empty cells if x and y are in inverse proportion. x: 16, 12, __, 36 and y: 9, __, 48, __.
- Therefore, to complete 5/3 units of work, it takes them 1 hour if they work together. How much time will it take them to complete 1 unit of work?
- Is the quantity of work and time taken to complete it directly or inversely proportional?
- Which of the following pairs of quantities are in inverse proportion? (i) The number of taps filling a water tank and the time taken to fill it. (ii) The number of painters hired and the days needed to paint a wall of fixed size. (iii) The distance a car can travel and the amount of petrol in the tank. (iv) The speed of a cyclist and the time taken to cover a fixed route. (v) The length of cloth bought and the price paid at a fixed rate per metre. (vi) The number of pages in a book and the time required to read it at a fixed reading speed.
- If 24 pencils cost ₹120, how much will 20 such pencils cost?
- A tank on a building has enough water to supply 20 families living there for 6 days. If 10 more families move in there, how long will the water last? What assumptions do you need to make to work out this problem?
- Fill in the average number of hours each living being sleeps in a day by looking at the charts. Select the appropriate hours from this list : 15, 2.5, 20, 8, 3.5, 13, 10.5, 18.
- The pie chart on the right shows the result of a survey carried out to find the modes of transport used by children to go to school. Study the pie chart and answer the following questions. (i) What is the most common mode of transport? (ii) What fraction of children travel by car? (iii) If 18 children travel by car, how many children took part in the survey? How many children use taxis to travel to school? (iv) By which two modes of transport are equal numbers of children travelling?
- Three workers can paint a fence in 4 days. If one more worker joins the team, how many days will it take them to finish the work? What are the assumptions you need to make?
- It takes 6 hours to fill 2 tanks of the same size with a pump. How long will it take to fill 5 such tanks with the same pump?
- A given set of chairs are arranged in 25 rows, with 12 chairs in each row. If the chairs are rearranged with 20 chairs in each row, how many rows does this new arrangement have?
- A school has 8 periods a day, each of 45 minutes duration. How long is each period, if the school has 9 periods a day, assuming that the number of school hours per day stays the same?
- A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If both pumps are used together, how long will the tank take to fill?
- A factory requires 42 machines to produce a given number of toys in 63 days. How many machines are required to produce the same number of toys in 54 days?
- A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car take if it travels at a speed of 80 km/h?
Chapter at a Glance
- Two ratios a : b and c : d are proportional when a × d = b × c. A ratio may have many terms: 8 : 4 : 2 : 1 says that whatever multiplies one term multiplies all of them.
- The RF (Representative Fraction) on a map, such as 1 : 60,00,000, is a ratio between two lengths, so it carries no unit — 1 cm on the map stands for 60,00,000 cm, that is 60 km, of straight-line ground distance.
- To divide a quantity x in the ratio a : b : c : …, add the terms and give each part its share: x × a/(a + b + c + …), x × b/(a + b + c + …), and so on.
- A pie chart divides 360° in the ratio of the data. Since 360° stands for the whole, each category gets an angle proportional to its count — one degree per person when 360 people are surveyed.
- Directly proportional quantities keep their quotient fixed: x₁/y₁ = x₂/y₂ = k. Inversely proportional quantities keep their product fixed: x₁y₁ = x₂y₂ = k.
- Whether a pair is direct or inverse is decided by the situation, not by a rule to memorise — ask what stays fixed. Fixed rate per item → direct. Fixed total job or fixed distance → inverse.
How to Download NCERT Solutions for Class 8 Maths Chapter 10 PDF
Follow these simple steps to get the Proportional Reasoning 2 questions-and-answers PDF from Ganita Prakash.
- Search NCERT Solutions for Class 8 Maths Chapter 10 aglasem and open this page.
- Read the exercise questions with answers for Proportional Reasoning 2 shown above.
- Click the Download PDF link to save the Proportional Reasoning 2 solutions to your device.
NCERT Solutions for Class 8 Maths – All Chapters
There are more chapters to study besides Proportional Reasoning 2 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 10 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.
NCERT Solutions for Class 8 Maths Chapter 10 – An Overview
The key highlights of this study material are as follows.
| Aspects | Details |
|---|---|
| Class | Class 8 |
| Subject | Maths |
| Chapter Number | Chapter 10 |
| Chapter Name | Proportional Reasoning 2 |
| Book Name | Ganita Prakash |
| Book By | NCERT (National Council of Educational Research and Training) |
| Educational Resource Here | NCERT Solutions of Class 8 Maths Chapter 10 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 10 Proportional Reasoning 2 – FAQs
What are the NCERT Solutions for Class 8 Maths Chapter 10 Proportional Reasoning 2?
They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 10 Proportional Reasoning 2 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 10 solutions PDF for free?
Open this page on aglasem, read the Proportional Reasoning 2 questions with answers, and click the “Download Solutions PDF” link. The Class 8 Maths Chapter 10 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 10 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 10 Proportional Reasoning 2, then please ask in the comments below.
