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Maths ·Class 8 Maths

Ganita Prakash Class 8 Solutions

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RBSEGuide
· Jun 02, 2026 · Reviewed & updated Sep 17, 2026 · 32 min read

Class 8 Ganita Prakash Solutions

Ganita Prakash Class 8 Part 1 Solutions

Class 8 Maths Ganita Prakash Solutions

Chapter 1 A Square and A Cube Class 8 Solutions

  1. Find the squares of the first 30 natural numbers and fill in the table below. Class 8
  2. What patterns do you notice? Share your observations and make conjectures. Class 8
  3. What do you notice about the number of zeros at the end of a number Class 8
  4. Find how many numbers lie between two consecutive perfect squares. Do you notice a pattern? Class 8
  5. Can you see any relation between triangular numbers and square numbers? Class 8
  6. Find whether 1156 and 2800 are perfect squares using prime factorisation. Class 8
  7. Which of the following numbers are not perfect squares? Class 8
  8. Find the length of the side of a square whose area is 441 m². Class 8
  9. How many numbers lie between the squares of the following numbers? Class 8
  10. How many tiny squares are there in the following picture? Write the prime factorisation Class 8
  11. How many cubes of side 1 cm will make a cube of side 3 cm? Class 8
  12. What patterns do you notice in the table above? Class 8
  13. Similar to squares, can you find the number of cubes with 1 digit, 2 digits, and 3 digits? Class 8
  14. The next two taxicab numbers after 1729 are 4104 and 13832. Find the two ways in which Class 8
  15. Find the cube roots of 27000 and 10648. Class 8
  16. State true or false. Explain your reasoning. The cube of any odd number is even. Class 8
  17. You are told that 1331 is a perfect cube. Can you guess without factorisation what its cube root is? Class 8
  18. A Square and A Cube Class 8 Notes
  19. A Square and a Cube Class 8 MCQ
  20. A Square and a Cube Class 8 Assertion and Reason Questions
  21. A Square and a Cube Class 8 Fill in the blanks
  22. A Square and a Cube Class 8 Very Short Question Answer
  23. A Square and a Cube Class 8 Short Question Answer
  24. A Square and a Cube Class 8 Long Question Answer

Chapter 2 Power Play Class 8 Solutions

  1. Now, what do you think the thickness would be after 30 folds? 45 folds? Make a guess. Class 8
  2. What is (-1)5? Is it positive or negative ? What about (-1)56? Class 8
  3. Write the following expressions as a power of a power in at least two different ways: Class 8
  4. What if Damayanti had changed the order in which she placed the flowers in the lakes? Class 8
  5. Express the following in exponential form: (i) 6 × 6 × 6 × 6 (ii) y × y Class 8
  6. Express each of the following as a product of powers of their prime factors in exponential form. Class 8
  7. Roxie has 7 dresses, 2 hats, and 3 pairs of shoes. How many different ways can Roxie dress up? Class 8
  8. How many passwords are possible with such a lock? Class 8
  9. What is 2100 ÷ 225 in powers of 2? In a generalised form, na ÷ nb = na – b Class 8
  10. Use the power line for 7 to answer the following questions. Class 8
  11. We had required a and b to be counting numbers. Can a and b be any integers? Will the generalised forms still hold true? Class 8
  12. Write these numbers in the same way: (i) 172, (ii) 5642, (iii) 6374. Class 8
  13. Roxie wonders, “Instead of jaggery if we use 1-rupee coins, how many coins are needed to equal my weight?”. How can we find out? Class 8
  14. Calculate and write the answer using scientific notation: How many ants are there for every human in the world? Class 8
  15. Calculate and write the answer using scientific notation: If one star is counted every second Class 8
  16. Find out the units digit in the value of 2224 ÷ 432? [Hint: 4 = 22] Class 8
  17. Write the given number as the product of two or more powers in three different ways. The powers can be any integers. Class 8
  18. Simplify and write these in the exponential form. (i) 10-2 × 10-5 (ii) 57 ÷ 54 (iii) 9-7 ÷ 94 Class 8
  19. Circle the numbers that are the same — 24 × 36 64 × 32 610 Class 8
  20. A dairy plans to produce 8.5 billion packets of milk in a year. They want a unique ID (identifier) code for each packet. Class 8
  21. A digital locker has an alpha-numeric (it can have both digits and letters) passcode of length 5. Class 8
  22. Calculate and write the answer in scientific notation: (i) If each person in the world had 30 pieces of clothing, Class 8
  23. Power Play Class 8 Notes
  24. Power Play Class 8 MCQ
  25. Power Play Class 8 Assertion and Reasoning Questions
  26. Power Play Class 8 Fill in the blanks
  27. Power Play Class 8 Very Short Question Answer
  28. Power Play Class 8 Long Question Answer

Chapter 3 A Story of Numbers Class 8 Solutions

  1. Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Class 8
  2. What could be the difficulties with using a number system that counts only in groups of a single particular size? Class 8
  3. A group of indigenous people in a Pacific island use different sequences of number names to count different objects. Class 8
  4. Consider the extension of the Gumulgal number system beyond 6 in the same way of counting by 2s. Come up with ways Class 8
  5. Represent the following numbers in the Egyptian system : 10458, 1023, 2660, 784, 1111, 70707. Class 8
  6. Write the following numbers in the above base-5 system using the symbols in Table 2 : 15, 50,137, 293, 651. Class 8
  7. Add the following Egyptian numerals: Class 8
  8. What is any landmark number multiplied by ∩ (that is 10)? Find the following products — Class 8
  9. Find the following products — Class 8
  10. Now find the following products — Class 8
  11. Create your own number system of base 4, and represent numbers from 1 to 16. Class 8
  12. Represent the following numbers in the Mesopotamian system — (i) 63 (ii) 132 (iii) 200 (iv) 60 (v) 3605 Class 8
  13. Why do you think the Chinese alternated between the Zong and Hehg symbols? If only the Zong symbols were to be used Class 8
  14. Where in your daily lives, and in which professions, do the Hindu numerals, and 0, play an important role? Class 8
  15. A Story of Numbers Class 8 Notes
  16. A Story of Numbers Class 8 MCQ
  17. A Story of Numbers Class 8 Assertion and Reasoning Questions
  18. A Story of Numbers Class 8 Fill in the blanks
  19. A Story of Numbers Class 8 Very Short Question Answer
  20. A Story of Numbers Class 8 Short Question Answer
  21. A Story of Numbers Class 8 Long Question Answer

Chapter 4 Quadrilaterals Class 8 Solutions

  1. Find all the other angles inside the following rectangles. Class 8
  2. Draw a quadrilateral whose diagonals have equal lengths of 8 cm that bisect each other, and intersect at an angle of Class 8
  3. We have seen how to get 90° using paper folding. Now, suppose we do not have any paper but two sticks Class 8
  4. Do the diagonals of a parallelogram intersect at a particular angle? Class 8
  5. Using the diagonal properties, construct a parallelogram whose diagonals are of lengths 7 cm and 5 cm Class 8
  6. Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm. Class 8
  7. Find the remaining angles in the following trapeziums — Class 8
  8. Draw a Venn diagram showing the set of parallelograms, kites, rhombuses, rectangles, and squares. Class 8
  9. Construct a square with diagonal 6 cm without using a protractor. Class 8
  10. CASE is a square. The points U, V, W and X are the midpoints of the sides of the square. What type of quadrilateral is UVWX? Class 8
  11. What type of a quadrilateral is one in which the opposite sides are equal? Justify your answer. Class 8
  12. State whether the following statements are true or false. Justify your answers. A quadrilateral whose diagonals are equal Class 8
  13. Quadrilaterals Class 8 Notes
  14. Quadrilaterals Class 8 MCQ
  15. Quadrilaterals Class 8 Assertion and Reasoning Questions
  16. Quadrilaterals Class 8 Fill in the blanks
  17. Quadrilaterals Class 8 Very Short Question Answer
  18. Quadrilaterals Class 8 Short Question Answer
  19. Quadrilaterals Class 8 Long Question Answer

Chapter 5 Number Play Class 8 Solutions

  1. Explore these questions and any others that may occur to you. Discuss them with the class. Class 8
  2. Now, take four other consecutive numbers. Place' the '+' and ‘-’ signs as you have done before. Find out the results Class 8
  3. Do these patterns occur no matter which 4 consecutive numbers are chosen? Is there a way Class 8
  4. Is there a way to explain why this happens? Think of the rules for parity Class 8
  5. Is the phenomenon of all the expressions having the same parity limited to taking 4 numbers? What do you think? Class 8
  6. Similarly, determine and explain which of the other expressions always give even numbers. Write a couple of examples Class 8
  7. Examine each of the following statements, and determine whether it is ‘Always true’, ‘Sometime's true’, ‘Never true’. Class 8
  8. Find a number that has a remainder of 3 when divided by 5. Write more such numbers. Class 8
  9. The sum of four consecutive numbers is 34. What are these numbers? Class 8
  10. For each statement below, determine whether it is always true, sometimes true, or never true. Explain your answer. Class 8
  11. Find a few numbers that leave a remainder of 2 when divided by 3 and a remainder of 2 when divided by 4. Class 8
  12. “I hold some pebbles, not too many, When I group them in 3’s, one stays with me. Class 8
  13. When divided by 7, the number 661 leaves a remainder of 3, and 4779 leaves a remainder of 5. Without calculating Class 8
  14. Find a number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4 Class 8
  15. Find, without dividing, whether the following numbers are divisible by 9. Class 8
  16. Find the multiple of 9 that is closest to the number 6000. Class 8
  17. Explore the remainders when powers of 10 are divided by 3. Explain why this method works. Class 8
  18. What could be a general method or shortcut to check divisibility by 11? Class 8
  19. Using this shortcut, find out whether the following numbers are divisible by 11. Further, find the remainder Class 8
  20. Fill in the following table. Find a quick way to do this? Class 8
  21. Will checking its divisibility by its factors 2 and 3 work? Use the shortcuts for 2 and 3 on these numbers Class 8
  22. Between the numbers 600 and 700, which numbers have the digital root : (i) 5 (ii) 7 (iii) 3 Class 8
  23. Now, find the digital roots of some consecutive multiples of (i) 3, (ii) 4, and (iii) 6. Class 8
  24. What are the digital roots of numbers that are 1 more than a multiple of 6? What do you notice? Try to explain the patterns noticed. Class 8
  25. I'm made of digits, each tiniest and odd, No shared ground with root #1 — how odd! Class 8
  26. Write any number. Generate a sequence of numbers by repeatedly adding 11, What would be the digital roots Class 8
  27. Make conjectures by examining if there are any patterns or relations between the parity of a number Class 8
  28. Solve the cryptarithms given below. Let us now try solving some cryptarithms Class 8
  29. Solve the following: (i) UT × 3 = PUT (ii) AB × 5 = BC (iii) L2N × 2 = 2NP (iv) XY × 4 = ZX Class 8
  30. If 31z5 is a multiple of 9, where z is a digit, what is the value of 2? Explain why there are two answers to this problem. Class 8
  31. When is the sum of two multiples of 3, a multiple of 6 and when is it not? Explain the different Class 8
  32. If 48a236 is a multiple of 18, list all possible pairs of values for a and 6. Class 8
  33. If 3p7q8 is divisible by 44, list all possible pairs of values for p and q. Class 8
  34. Find three consecutive numbers such that the first number is a multiple of 2, the second number Class 8
  35. The middle number in the sequence of 5 consecutive even numbers is 5p. Express the other Class 8
  36. Determine whether the statements below are ‘Always True’, ‘Sometimes True’, or ‘Never True’. Explain your reasoning. Class 8
  37. Choose any 3 numbers. When is their sum divisible by 3? Explore all possible cases and generalise. Class 8
  38. Solve the cryptarithms — (i) EF × E = GGG (ii) WOW × 5 = OEOW Class 8
  39. Number Play Class 8 Notes
  40. Number Play Class 8 MCQ
  41. Number Play Class 8 Assertion and Reasoning Questions
  42. Number Play Class 8 Fill in the blanks
  43. Number Play Class 8 Very Short Question Answer
  44. Number Play Class 8 Short Question Answer
  45. Number Play Class 8 Long Question Answer

Chapter 6 We Distribute, Yet Things Multiply Class 8 Solutions

  1. Will the product always increase? Find 3 examples where the product decreases. Class 8
  2. Observe the multiplication grid below. Each number inside the grid is formed by multiplying two numbers. Class 8
  3. Expand the following products. (i) (3 + u) (v - 3) (ii) 2/3(15 + 6a) (iii) (10a + b) (10c + d) Class 8
  4. Find 3 examples where the product of two numbers remains unchanged when one of them is increased Class 8
  5. Expand (i) (a - b) (a + b), (ii) (a - b) (a² + ab + b²) and (iii) (a - b)(a³ + a²b + ab² + b³), Do you see a pattern? Class 8
  6. Describe a general rule to multiply a number (of any number of digits) by 11 and write the product in one line. Evaluate Class 8
  7. What could be a general rule to multiply a number by 101 and write the product in one line? Extend Class 8
  8. If a and b are any two integers, is (a + b)² always greater than a² + b²? If not, when is it greater? Class 8
  9. Use Identity 1A to write the expressions for the following. (i) (m + 3)² (ii) (6 + p)² Class 8
  10. Find the general expansion of (a - b)² using geometry, as we did for 55². Class 8
  11. Expand the following using both Identity 1B and by applying the distributive property (i) (b - 6)² (ii)(-2a + 3)² Class 8
  12. Use Identity 1C to calculate 98 × 102, and 45 × 55. Class 8
  13. Find 406², 72², 145², 1097², and 124² using the identities you have learnt so far. Class 8
  14. Use this formula to find the number of circles in Step 15. Class 8
  15. Write an algebraic expression for the number of tiles in Step n. Share your methods with the class. Class 8
  16. Write an expression for the area of the dashed region in the figure below. Use more than one method Class 8
  17. Compute these products using the suggested identity. (i) 46² using Identity 1A for (a + b)² Class 8
  18. Use either a suitable identity or the distributive property to find each of the following products. (i) (p - 1) (p + 11) Class 8
  19. For each statement identify the appropriate algebraic expression(s). Class 8
  20. Consider any 2 by 2 square of numbers in a calendar, as shown in the figure. Find products of numbers Class 8
  21. Verify which of the following statements are true. (i) (k + 1) (k + 2) - (k + 3) is always 2. Class 8
  22. A number leaves a remainder of 3 when divided by 7, and another number leaves a remainder Class 8
  23. What is the algebraic expression describing the following steps — add any two numbers. Class 8
  24. A tiny park is coming up in Dhauli. The plan is shown in the figure. The two square plots each of area Class 8
  25. For each pattern shown below, (i) Draw the next figure in the sequence. (ii) How many basic units are there in Step 10? Class 8
  26. We Distribute, Yet Things Multiply Class 8 Notes
  27. We Distribute, Yet Things Multiply Class 8 MCQ
  28. We Distribute, Yet Things Multiply Class 8 Assertion and Reasoning Questions
  29. We Distribute, Yet Things Multiply Class 8 Fill in the blanks
  30. We Distribute, Yet Things Multiply Class 8 Very Short Question Answer
  31. We Distribute, Yet Things Multiply Class 8 Short Question Answer
  32. We Distribute, Yet Things Multiply Class 8 Long Question Answer

Chapter 7 Proportional Reasoning 1 Class 8 Solutions

  1. Why is this coffee lighter? Class 8
  2. Circle the following statements of proportion that are true. Class 8
  3. Fill in the missing numbers for these ratios that are proportional to 18 : 24. Class 8
  4. The following figure shows a small portion of a long brick wall with patterns made using coloured bricks. Class 8
  5. The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week? Class 8
  6. Divide ₹ 4,500 into two parts in the ratio 2 : 3. Class 8
  7. Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint Class 8
  8. I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. Class 8
  9. Anagh mixes 600 mL of orange juice with 900 mL of apple juice to make a fruit drink. Write the ratio Class 8
  10. 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 Class 8
  11. Let us try an ancient problem from Lilavati. At that time weights were measured in a unit named palas and niskas Class 8
  12. Harmain is a 1-year-old girl. Her elder brother is 5 years old. What will be Harmain’s age when the ratio Class 8
  13. 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, Class 8
  14. 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 Class 8
  15. A tractor can plough the same area of a field 4 times faster than a pair of oxen. A farmer wants to plough Class 8
  16. Proportional Reasoning 1 Class 8 Notes
  17. Proportional Reasoning 1 Class 8 MCQ
  18. Proportional Reasoning 1 Class 8 Assertion and Reasoning Questions
  19. Proportional Reasoning 1 Class 8 Fill in the blanks
  20. Proportional Reasoning 1 Class 8 Very Short Question Answer
  21. Proportional Reasoning 1 Class 8 Short Question Answer
  22. Proportional Reasoning 1 Class 8 Long Question Answer

Ganita Prakash Class 8 Part 2 Solutions

Class 8th Ganita Prakash Solutions

Chapter 1 Fractions in Disguise Class 8 Solutions

  1. Can you tell what percentage of the colour was made using yellow? Class 8
  2. Express the following fractions as percentages. (i) 3/5 (ii) 7/14 (iii) 9/20 (iv) 72/150 (v) 1/3 Class 8
  3. In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking? Class 8
  4. Pairs of quantities are. shown below. Identify and write appropriate symbols ;>', '<', "=' in the blanks. Try to do it without calculations. Class 8
  5. Try to calculate (without using pen and paper) the indicated percentages of the values shown in the table below. Class 8
  6. How did you find these values? Discuss the methods with the class. Do you find anything interesting in the table? Class 8
  7. Using this observation, mentally calculate how much 15% of the values in the table would be. Class 8
  8. Similarly, to find 10% of a quantity, what decimal value should be multiplied? Class 8
  9. In the next two days, he made ₹ 5000 and ₹ 6000 respectively. What percentage of his target are these values? Class 8
  10. On Day 7, he achieved 150% of his target. On Day 8, he achieved 210% of his target. Find the sales made on these days. Class 8
  11. Find the missing numbers. The first problem has been worked out. Class 8
  12. Find the value of the following and also draw their bar models. Class 8
  13. Surya made 60 ml of deep orange paint, how much red paint did he use if red paint made up Class 8
  14. Fill in the blanks appropriately : (i) 30% of k is 70, 60% of k is, 90% of k is, 120% of k is. Class 8
  15. Is 10% of a day longer than 1% of a week? Create such questions and challenge your peers. Class 8
  16. Workers in a coffee plantation take 18 days to pick coffee berries in 20% of the plantation. Class 8
  17. An estimated 90% of the world’s population lives in the Northern Hemisphere. Find the (approximate) number of people Class 8
  18. Complete this table by calculating the percentages to answer the questions : Class 8
  19. Find the profit percentage of the wholesaler and the manufacturer. Class 8
  20. She sells crayon boxes at ₹ 50 per box with a profit margin of 25%. How much did Shambhavi buy them from the wholesaler? Class 8
  21. Due to heavy rains, Snehal could not transport strawberries to Hyderabad from his farm in Panchgani. Class 8
  22. Check if the calculations are correct in the bill shown. Class 8
  23. I am a carpenter and I make chairs. The cost of materials for a chair is ? 475 and I want to have a profit Class 8
  24. A clothing shop offers a 25% discount on all shirts. If the original price of a shirt is ₹300, how much Class 8
  25. Samson bought a car for ₹ 4,40,000 after getting a 15% discount from the car dealer. What was the original price of the car? Class 8
  26. The price of 1 kg of rice was ₹ 38 in 2024. It is ₹ 42 in 2025. What is the rate of inflation? Class 8
  27. A milkman sold two buffaloes for ₹ 80,000 each. On one of them, he made a profit of 5% and on the other a loss Class 8
  28. Which of the following statement(s) mean the same as — “The demand for cameras has fallen by 85% in the last decade”? Class 8
  29. Bank of Wahapur offers an interest of 5% p.a. Compare how much one gets if one deposits ₹ 20,000 for a period Class 8
  30. Suppose we want to know the expression/formula to find the total interest amount gained at the end Class 8
  31. The post office offers an interest of 7% p.a. How much interest would one get if one invests ₹ 50,000 for 3 years without compounding? Class 8
  32. Consider an amount ₹ 1000. If this grows at 10% p.a., how long will it take to double when compounding is done vs. when Class 8
  33. In a laboratory, the number of bacteria in a certain experiment increases at the rate of 2.5% per hour. Class 8
  34. A provision store is offering a stock clearance sale. Customers can choose one of the two options 20% discount or ₹ 50 discount Class 8
  35. The population of Bengaluru in 2025 is about 250% of its population in 2000. If the population in 2000 was 50 lakhs Class 8
  36. The price of a mobile phone is ₹ 8,250. A GST of 18% is added to the price. Which of the following gives the final price Class 8
  37. A shopkeeper initially set the price of a product with a 35% profit margin. Due to poor sales, he decided to offer Class 8
  38. What is 5% of 40? What is 40% of 5? What is 25% of 12? What is 12% of 25? What is 15% of 60? What is 60% of 15? Class 8
  39. A shopkeeper sells pencils at a price such that the selling price of 3 pencils is equal to the cost of 5 pencils. Class 8
  40. If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by? Class 8
  41. Three shops sell the same items at the same price. The shops offer deals as follows: Class 8
  42. In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring Class 8
  43. Fractions in Disguise Class 8 Notes
  44. Fractions in Disguise Class 8 MCQ
  45. Fractions in Disguise Class 8 Assertion and Reasoning Questions
  46. Fractions in Disguise Class 8 Fill in the blanks
  47. Fractions in Disguise Class 8 Short Question Answer
  48. Fractions in Disguise Class 8 Long Question Answer

Chapter 2 The Baudhayana-Pythagoras Theorem Class 8 Solutions

  1. Why should the extension of the vertical and horizontal sides of the original square pass through the vertices of the dotted square? Class 8
  2. Cut out a square from a piece of paper. Now make a square whose area is half the area of the first square. Class 8
  3. Explain by connecting QS and PR, finding the different angles formed, and then using tringle congruence. Class 8
  4. The length of the two equal sides of an isosceles right triangle is given. Find the length of the hypotenuse. Class 8
  5. The hypotenuse of an isosceles right triangle is 10. What are its other two sidelengths? Class 8
  6. If a right-angled triangle has shorter sides of lengths 5 cm and 12 cm, then what is the length of its hypotenuse? Class 8
  7. Using the constructions you have now seen, how would you construct a square whose area is triple the area of a given square? Class 8
  8. Let a, b and c denote the length of the sides of a right triangle, with c being the length of the hypotenuse. Class 8
  9. List down all the Baudhayana triples with numbers less than or equal to 20. Class 8
  10. Can we further generalise the conjecture? Class 8
  11. If (a, b, c) is non-primitive, and the integers have f greater than 1 as a common factor Class 8
  12. Find 5 more Baudhayana triples using this idea. Class 8
  13. Are there primitive triples that cannot be obtained through this method? Class 8
  14. Find the side length of a rhombus whose diagonals are of length 24 units and 70 units. Class 8
  15. Give 5 examples of rectangles whose sidelengths and diagonals are all integers. Class 8
  16. (i) Using the dots of a grid as the vertices, can you create a square that has an area of (a) 2 sq. units, (b) 3 sq. units Class 8
  17. The Baudhayana-Pythagoras Theorem Class 8 Notes
  18. The Baudhayana-Pythagoras Theorem Class 8 MCQ
  19. The Baudhayana-Pythagoras Theorem Class 8 Assertion and Reasoning Questions
  20. The Baudhayana-Pythagoras Theorem Class 8 Fill in the blanks
  21. The Baudhayana-Pythagoras Theorem Class 8 Very Short Question Answer
  22. The Baudhayana-Pythagoras Theorem Class 8 Short Question Answer
  23. The Baudhayana-Pythagoras Theorem Class 8 Long Question Answer

Chapter 3 Proportional Reasoning 2 Class 8 Solutions

  1. A cricket coach schedules practice sessions that include different activities in a specific ratio — time for warm-up/ cool-down Class 8
  2. 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. Class 8
  3. Can you construct a triangle with sidelengths in the ratio 1 : 3 : 5? Why or why not? Class 8
  4. 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 Class 8
  5. The following table shows the time taken to travel from Lucknow to Kanpur using different modes of transport: Class 8
  6. Which of these inverse proportion? Class 8
  7. Which of the following pairs of quantities are in inverse proportion? (i) The number of taps filling a water tank and the time Class 8
  8. A tank on a building has enough water to supply 20 families living there for 6 days. If 10 more families move in there Class 8
  9. The pie chart given below shows the result of a survey carried out to find the modes of transport used by children to go to school. Class 8
  10. 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? Class 8
  11. 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 Class 8
  12. A factory requires 42 machines to produce a given number of toys in 63 days. How many machines are required to produce Class 8
  13. Proportional Reasoning 2 Class 8 Notes
  14. Proportional Reasoning 2 Class 8 MCQ
  15. Proportional Reasoning 2 Class 8 Assertion and Reasoning Questions
  16. Proportional Reasoning 2 Class 8 Fill in the blanks
  17. Proportional Reasoning 2 Class 8 Very Short Question Answer
  18. Proportional Reasoning 2 Class 8 Short Question Answer
  19. Proportional Reasoning 2 Class 8 Long Question Answer

Chapter 4 Exploring Some Geometric Themes Class 8 Solutions

  1. Draw the initial few steps (at least till Step 2) of the shape sequence that leads to the Sierpinski Triangle. Class 8
  2. Draw the initial few steps (at least till Step 2) of the shape sequence that leads to the Koch Snowflake. Class 8
  3. If the congruent polygons of a prism have 10 sides, how many faces, edges and vertices does the prism have? Class 8
  4. Which of the following are the nets of a cube? First, try to answer by visualisation. Then, you may use cutouts and try. Class 8
  5. Draw a net of a cuboid having sidelengths: (i) 5 cm, 3 cm, and 1 cm (ii) 6 cm, 3 cm, and 2 cm Class 8
  6. What are the sidelengths of the rectangle obtained? Class 8
  7. Can you now compare the lengths p and l? Class 8
  8. What do you think is the projection of a parallelogram under different orientations? Class 8
  9. Find the front view, top view and side view of each of the following solids, fixing its orientation with respect to the vertical Class 8
  10. Draw the top view, front view and the side view of each of the following combinations of identical cubes. Class 8
  11. Which solid corresponds to the given top view, front view, and side view? Class 8
  12. What are the different shapes the projection of a cube can make under different orientations? Class 8
  13. Is there anything strange about the path of this ball? Recreate it on the isometric grid. Class 8
  14. Exploring Some Geometric Themes Class 8 Notes
  15. Exploring Some Geometric Themes Class 8 MCQ
  16. Exploring Some Geometric Themes Class 8 Assertion and Reasoning Questions
  17. Exploring Some Geometric Themes Class 8 Fill in the blanks
  18. Exploring Some Geometric Themes Class 8 Very Short Question Answer
  19. Exploring Some Geometric Themes Class 8 Short Question Answer
  20. Exploring Some Geometric Themes Class 8 Long Question Answer

Chapter 5 Tales by Dots and Lines Class 8 Solutions

  1. Calculate and mark the mean of each collection of data below? Class 8
  2. Can there be more than one such ‘centre’? In other words, is there any other value such that the sum of the distances Class 8
  3. Explore if it is possible to include or remove 2 values such that the mean is unchanged. Class 8
  4. Consider the data: 8, 3, 10, 13, 4, 6, 7, 7, 8, 8, 5. Calculate its mean. Class 8
  5. The mean of the new collection also increases by 10. Notice that the relative position of the mean stays the same. Class 8
  6. Will including a new value to the data increase or decrease the median? Class 8
  7. Find out if the class average marks in Odia is greater than the class average marks in Telugu. Class 8
  8. The dot plot below shows a collection of data and its average; but one dot is missing. Mark the missing value so that the mean Class 8
  9. The three dot plots below show the lengths, in minutes, of songs of different albums. Which of these has a mean of 5.57 minutes? Class 8
  10. Examine the statements below and justify if the statement is always true, sometimes true, or never true. Class 8
  11. Consider the data : 12, 47, 8, 73, 18, 35, 39, 8, 29, 25, p. Which of the following number(s) could be p if the median of this data is 29? Class 8
  12. A dart-throwing competition was organised in a school. The number of throws participants took to hit the bull’s eye Class 8
  13. Why are the trends so distinct in these two states? What factors determine a region’s temperature? Class 8
  14. What would a plot of the monthly minimum temperatures for these states look like? Class 8
  15. The average number of customers visiting a shop and the average number of customers actually purchasing Class 8
  16. The following line graph shows the number of births in every month in India over a time period : Class 8
  17. Moan Grids : (i) Fill the grid with 9 distinct numbers such that the average along each row, column, and diagonal is 10. Class 8
  18. Fill in the blanks such that the median of the collection is 13 : 5, 21, 14, How many possibilities exist Class 8
  19. There were 2 new admissions to Sudhakar’s class just a couple of days after the class average height was found to be 150.2 cm. Class 8
  20. Is 17 the average of the data shown in the dot plot below? Share the method you used to answer this question. Class 8
  21. The following table shows the retail price (in ₹) of iodised salt in the month of January in a few states over 10 years. Class 8
  22. Answer the following questions based on the line graph. (i) How long do children aged 10 in urban areas spend Class 8
  23. Small group project: Make a group of 3-4 members. Do at least one of the following: (i) Track daily sleep time Class 8
  24. The following graphs show the sunrise and sunset times across the year at 4 locations in India. Observe how the graphs Class 8
  25. Tales by Dots and Lines Class 8 Notes
  26. Tales by Dots and Lines Class 8 MCQ
  27. Tales by Dots and Lines Class 8 Assertion and Reasoning Questions
  28. Tales by Dots and Lines Class 8 Fill in the blanks
  29. Tales by Dots and Lines Class 8 Very Short Question Answer
  30. Tales by Dots and Lines Class 8 Short Question Answer
  31. Tales by Dots and Lines Class 8 Long Question Answer

Chapter 6 Algebra Play Class 8 Solutions

  1. How would you change this game to make the final answer 3? What about 5? Class 8
  2. Can you change the steps in this trick and still find the original date? Instead of subtracting 165 from the final answer Class 8
  3. Fill the following pyramids : Class 8
  4. Without building the entire pyramid, find the number in the topmost row given the bottom row in each of these cases. Class 8
  5. What can you say about the numbers in the pyramid and the number at the top in the following cases? Class 8
  6. In the following grids, find the values of the shapes and fill in the empty squares: Class 8
  7. Can you work out what happens if a > b? Class 8
  8. In the trick given above, instead of finding the difference of the two 2-digit numbers, find their sum. What will happen? For example : Class 8
  9. Consider any 3-digit number, say abc. Make it a 6-digit number by repeating the digits, that is abcabc. Class 8
  10. There are 3 shrines, each with a magical pond in the front. If anyone dips flowers into these magical ponds Class 8
  11. A farm has some horses and hens. The total number of heads of these animals is 55 and the total number of legs Class 8
  12. Two friends, Gauri and Naina, are cowherds. One day, they pass each other on the road with their cows. Class 8
  13. I run a small dosa cart and my expenses are as follows : Rent for the dosa cart is ? 5000 per day. Class 8
  14. Evaluate the following sequence of fractions : What do you observe? Can you explain why this happens? Class 8
  15. (i) How many coins did Karim initially have? (ii) For what cost per round should Karim agree to the deal Class 8
  16. Algebra Play Class 8 Notes
  17. Algebra Play Class 8 MCQ
  18. Algebra Play Class 8 Assertion and Reasoning Questions
  19. Algebra Play Class 8 Fill in the blanks
  20. Algebra Play Class 8 Very Short Question Answer
  21. Algebra Play Class 8 Short Question Answer
  22. Algebra Play Class 8 Long Question Answer

Chapter 7 Area Class 8 Solutions

  1. Why do we count the number of unit squares to assign measures for area? Couldn’t we have just used the perimeter Class 8
  2. Identify the missing sidelengths. Class 8
  3. The figure shows a path (the shaded portion) laid aznd a rectangular park EFGH. Class 8
  4. The figure shows a plot with sides 14 m and 12 m, and with a crosspath. What other measurements do you need to find Class 8
  5. Find the area of the spiral tube shown in the figure. The tube has the same width throughout. Class 8
  6. In this figure, if the sidelength of the square is doubled, what is the increase in the areas of the regions 1, 2 and 3? Give reasons. Class 8
  7. Divide a square into 4 parts by drawing two perpendicular lines inside the square as shown in the figure. Class 8
  8. Find the area of ∆XDC. Class 8
  9. Find the length of the altitude BY. Class 8
  10. In the Sulba-Sutras, which are ancient Indian geometric texts that deal with the construction of altars Class 8
  11. [Sulb a-Sutras] Give a method to transform a triangle into a rectangle of equal area. Class 8
  12. ABCD, BCEF, and BFGH are identical squares. (i) If the area of the red region is 49 sq. units Class 8
  13. If M and N are the midpoints of XY and XZ, what fraction of the area of ∆XYZ is the area of ∆XMN? [Hint: Join NY] Class 8
  14. Find the area of the quadrilateral ABCD given that AC = 22 cm, BM = 3 cm, DN = 3 cm, BM is perpendicular to AC, and DN is perpendicular to AC. Class 8
  15. What measurements would you need to find the area of a regular hexagon? Class 8
  16. Give a method to obtain a quadrilateral whose area is half that of a given quadrilateral. Class 8
  17. Find the areas of the following parallelograms: Class 8
  18. Consider a rectangle and a parallelogram of the same sidelengths : 5 cm and 4 cm. Which has the greater area Class 8
  19. [Sulba-Sutras] Give a method to obtain a rectangle of the same area as a given triangle. Class 8
  20. [Sulba-Sutras] Give a method to convert a rectangle into an isosceles triangle by dissection. Class 8
  21. Find the area of a rhombus whose diagonals are 20 cm and 15 cm. Class 8
  22. Find the areas of the following figures : Class 8
  23. Here is one of the ways to convert trapezium ABCD into a rectangle EFGH of equal area— Class 8
  24. A regular hexagon is divided into a trapezium, an equilateral triangle, and a rhombus, as shown. Find the ratio of their areas. Class 8
  25. What do you think is the area of an A4 sheet? Its sidelengths are 21 cm and 29.7 cm. Now find its area. Class 8
  26. Express the following lengths in inches : Class 8
  27. How many m² is a km² ? Class 8
  28. Area Class 8 Notes
  29. Area Class 8 MCQ
  30. Area Class 8 Assertion and Reasoning Questions
  31. Area Class 8 Fill in the blanks
  32. Area Class 8 Very Short Question Answer
  33. Area Class 8 Short Question Answer
  34. Area Class 8 Long Question Answer