NCERT Solutions for Class 8 Maths Chapter 13 Algebra Play provide clear, step-by-step answers to every exercise and in-text question from the chapter Algebra Play 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 13 question-answer PDF.
NCERT Solutions for Class 8 Maths Chapter 13 Algebra Play
- Class: Class 8
- Subject: Maths
- Chapter: Chapter 13 – Algebra Play
- Textbook: Ganita Prakash (NCERT)
- Study material: NCERT Solutions – questions with answers, free PDF
These solutions answer all the exercise questions of Chapter 13 Algebra Play — 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 13 Algebra Play View Download
NCERT Solutions for Class 8 Maths Chapter 13 PDF Download
You can read the NCERT Solutions for Class 8 Maths Chapter 13 online above, or download the complete question-answer PDF to study Algebra Play offline at any time.
NCERT Solutions for Class 8 Maths Chapter 13 PDF Download Link – Click Here to Download Solutions PDF
Questions Covered in This Chapter
These NCERT Solutions answer all 43 questions of this chapter. The questions solved are:
- I predict you get 2. Am I right? Try it out with different starting numbers. Do you always end up with the same value, 2? Why?
- How would you change this game to make the final answer 3? What about 5?
- Can you come up with more complicated steps that always lead to the same final value?
- How did Shubham figure out the date chosen by Mukta?
- Mukta thinks of another date, follows the same steps, and reports her answer as 1390. What date did Mukta start with this time?
- Find the dates if the final answers are the following: (i) 1269 (ii) 394 (iii) 296
- Can you change the steps in this trick and still find the original date? Instead of subtracting 165 from the final answer, you might have to subtract some other number.
- Try to devise your own ‘Think of a Number’ trick.
- Use the same rule to fill these pyramids: (i) bottom row 6, 2 (ii) bottom row 3, 4, 3 (iii) bottom row 5, 4, 5, 0
- How do we fill this pyramid? (top 10; middle row 4, ?; bottom row 1, ?, ?)
- What about filling in the numbers in this pyramid? Where do we start? (top 60; middle row ?, ?; bottom row 12, ?, 8)
- Fill the following pyramids: (i) four rows — top 50, second row right box 22, bottom row 4, ?, 6, ? (ii) four rows — second row left box 40, third row right box 9, bottom row 5, ?, 7, ? (iii) four rows — top 35, third row right box 7, bottom row 3, 5, ?, ?
- What is the relationship between the numbers in the bottom row and the number at the top?
- What about a pyramid with three rows? Using letter numbers for the bottom row, we can write an expression for the top row.
- Without building the entire pyramid, find the number in the topmost row given the bottom row in each of these cases. (i) 4, 13, 8 (ii) 7, 11, 3 (iii) 10, 14, 25
- Write an expression for the topmost row of a pyramid with 4 rows in terms of the values in the bottom row.
- Without building the entire pyramid, find the number in the topmost row given the bottom row in each of these cases. (i) 8, 19, 21, 13 (ii) 7, 18, 19, 6 (iii) 9, 7, 5, 11
- If the first three Virahāṅka-Fibonacci numbers are written in the bottom row of a number pyramid with three rows, fill in the rest of the pyramid. What numbers appear in the grid? What is the number at the top? Are they all Virahāṅka-Fibonacci numbers?
- What can you say about the numbers in the pyramid and the number at the top in the following cases? (i) The first four Virahāṅka-Fibonacci numbers are written in the bottom row of a four row pyramid. (ii) The first 29 Virahāṅka-Fibonacci numbers are written in the bottom row of a 29 row pyramid.
- If the bottom row of an n row pyramid contains the first n Virahāṅka-Fibonacci numbers, what can we say about the numbers in the pyramid? What can we say about the number at the top?
- Can we find the 4 numbers in the grid from just knowing this sum?
- Suppose you are told that the sum is 36. Can you find the 4 numbers in the grid?
- Create your own calendar trick. For instance, choose a grid of a different size and shape.
- In the following grid, shapes represent numbers. In each row, the last column is the sum of the values to its left. How do we find the values of the shapes?
- In the following grids, find the values of the shapes and fill in the empty squares.
- Fill the digits 2, 3, and 5 in ⬜⬜ × ⬜, using each digit once. What is the largest product possible?
- How do we find the largest product among these six options?
- In this case, we used the largest digit as the multiplier. The other two digits were arranged in decreasing order to form the multiplicand. Will this always be the case? Let us find out using algebra.
- Fill the digits 1, 3, and 7 in ⬜⬜ × ⬜ to make the largest product possible.
- Fill the digits 3, 5, and 9 in ⬜⬜ × ⬜ to make the largest product possible.
- If we choose other 2-digit numbers, and follow the steps, will there always be no remainder?
- Can you work out what happens if a > b?
- In the trick given above, what is the quotient when you divide by 9? Is there a relationship between the two numbers and the quotient?
- In the trick given above, instead of finding the difference of the two 2-digit numbers, find their sum. What will happen? For example: We start with 31. After reversing we get 13. Adding 31 and 13, we get 44. We start with 28. After reversing we get 82. Adding 28 and 82, we get 110. We start with 12. After reversing we get 21. Adding 12 and 21, we get 33. Observe that all these numbers are divisible by 11. Is this always true? Can we justify this claim using algebra?
- Consider any 3-digit number, say abc (100a + 10b + c). Make two other 3-digit numbers from these digits by cycling these digits around, yielding bca and cab. Now add the three numbers. Using algebra, justify that the sum is always divisible by 37. Will it also always be divisible by 3? [Hint: Look at some multiples of 37.]
- Consider any 3-digit number, say abc. Make it a 6-digit number by repeating the digits, that is abcabc. Divide this number by 7, then by 11, and finally by 13. What do you get? Try this with other numbers. Figure out why it works. [Hint: Multiply 7, 11 and 13.]
- There are 3 shrines, each with a magical pond in the front. If anyone dips flowers into these magical ponds, the number of flowers doubles. A person has some flowers. He dips them all in the first pond and then places some flowers in shrine 1. Next, he dips the remaining flowers in the second pond and places some flowers in shrine 2. Finally, he dips the remaining flowers in the third pond and then places them all in shrine 3. If he placed an equal number of flowers in each shrine, how many flowers did he start with? How many flowers did he place in each shrine?
- A farm has some horses and hens. The total number of heads of these animals is 55 and the total number of legs is 150. How many horses and how many hens are on the farm? Can you solve this without letter-numbers? [Hint: If all the 55 animals were hens, then how many legs would there be? Using the difference between this number and 150, can you find the number of horses?]
- A mother is 5 times her daughter’s age. In 6 years’ time, the mother will be 3 times her daughter’s age. How old is the daughter now?
- Two friends, Gauri and Naina, are cowherds. One day, they pass each other on the road with their cows. Gauri says to Naina, “You have twice as many cows as I do”. Naina says, “That’s true, but if I gave you three of my cows, we would each have the same number of cows”. How many cows do Gauri and Naina have?
- I run a small dosa cart and my expenses are as follows: Rent for the dosa cart is ₹5000 per day. The cost of making one dosa (including all the ingredients and fuel) is ₹10. (i) If I can sell 100 dosas a day, what should be the selling price of my dosa to make a profit of ₹2000? (ii) If my customers are willing to pay only ₹50 for a dosa, how many dosas should I aim to sell in a day to make a profit of ₹2000?
- Evaluate the following sequence of fractions: 1/3, (1 + 3)/(5 + 7), (1 + 3 + 5)/(7 + 9 + 11). What do you observe? Can you explain why this happens? [Hint: Recall what you know about the sum of the first n odd numbers.]
- Karim and the Genie. Karim was taking a nap under a tree. He had a dream about a magical lamp and a genie… The genie said, “Do you see the banyan tree over there? All you have to do is go around it once. The money in your pocket will double”, and then, “Since I am bringing you great riches, you should share some of your gains with me. You must give me 8 coins each time you go around the tree.” He went around the tree once and the number of coins doubled; he gave 8 coins to the genie. He made another round; again the number doubled and he gave 8 more coins. He went around the tree for the third time. The number of coins doubled again, but to his horror, he was left with only 8 coins, exactly the number of coins he owed the genie! (i) How many coins did Karim initially have? (ii) For what cost per round should Karim agree to the deal, if he wants to increase the number of coins he has? (iii) Through its magical powers, the genie knows the number of coins that Karim has. How should the genie set the cost per round so that it gets all of Karim’s coins?
Chapter at a Glance
- A letter-number stands for every possible starting value at once . That is why one line of algebra settles a trick that no amount of trying out numbers can ever settle — testing 100 starting numbers only tests 100 of them.
- Solving an equation means doing the same thing to both sides — adding, subtracting, multiplying or dividing by the same amount. The two sides name one number, so an operation applied to both keeps them naming one number. That is the whole justification for every step.
- Modelling a word situation means naming the unknown, then translating each sentence into an equation about it. “The mother is 5 times her daughter’s age” becomes m = 5d; “in 6 years” becomes d + 6 and m + 6.
- In a number pyramid each box is the sum of the two below it. Read forwards it is addition; read backwards it is subtraction — and when no box has both its neighbours known, letter-numbers finish the job.
- The top of an n-row pyramid is a fixed combination of the bottom row: a + b for 2 rows, a + 2b + c for 3, a + 3b + 3c + d for 4. Each bottom entry is counted once for every way of climbing from it to the top.
- Place value is what most of these tricks really use. A two-digit number is 10a + b, so reversing it and subtracting leaves 9(b – a); adding leaves 11(a + b); cycling the digits of 100a + 10b + c leaves 111(a + b + c) = 3 × 37 × (a + b + c).
- The same habit answers optimisation questions. With digits p < q < r, the largest product of the form ⬜⬜ × ⬜ is always (10q + p) × r — largest digit as the multiplier, the other two in decreasing order — and algebra proves it for all digit sets, not just the one you tried.
How to Download NCERT Solutions for Class 8 Maths Chapter 13 PDF
Follow these simple steps to get the Algebra Play questions-and-answers PDF from Ganita Prakash.
- Search NCERT Solutions for Class 8 Maths Chapter 13 aglasem and open this page.
- Read the exercise questions with answers for Algebra Play shown above.
- Click the Download PDF link to save the Algebra Play solutions to your device.
NCERT Solutions for Class 8 Maths – All Chapters
There are more chapters to study besides Algebra Play 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 13 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 13 – An Overview
The key highlights of this study material are as follows.
| Aspects | Details |
|---|---|
| Class | Class 8 |
| Subject | Maths |
| Chapter Number | Chapter 13 |
| Chapter Name | Algebra Play |
| Book Name | Ganita Prakash |
| Book By | NCERT (National Council of Educational Research and Training) |
| Educational Resource Here | NCERT Solutions of Class 8 Maths Chapter 13 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 13 Algebra Play – FAQs
What are the NCERT Solutions for Class 8 Maths Chapter 13 Algebra Play?
They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 13 Algebra Play 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 13 solutions PDF for free?
Open this page on aglasem, read the Algebra Play questions with answers, and click the “Download Solutions PDF” link. The Class 8 Maths Chapter 13 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 13 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 13 Algebra Play, then please ask in the comments below.
