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Class 8 Maths: Algebra Play, 8 practice questions with answers

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These are 8 practice questions on Chapter 6, Algebra Play, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover whether two orders of steps can give the same result, which tops a number pyramid can have, four consecutive numbers, numbers equal to 4 times their digit sum, five consecutive numbers, two taxi fares, the numbers that give 63 after taking away their digit sum, and a two-digit number with a condition on its digits. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-worked by a test script and each question was compared with the chapter's examples, activities and exercises, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 8, Part 2, Chapter 6, printed pages 135 to 147):

Tricks, pyramids and grids

Question 1. Asha's rule is "add 5, then multiply by 4". Bilal's rule is "multiply by 4, then add 5". They both start from the same number. (a) Using a letter-number, write each result. (b) Can the two results ever be equal? By how much do they always differ?

Answer: (a) 4x + 20 and 4x + 5; (b) never; Asha's is always 15 more. (a) Call the starting number x. Asha: x + 5, then 4(x + 5) = 4x + 20. Bilal: 4x, then 4x + 5. (b) The difference is (4x + 20) − (4x + 5) = 15 for every x, so the two results are never equal. For example, from 6: Asha gets 44 and Bilal gets 29. The order of the steps matters because the 5 is multiplied by 4 in Asha's rule but not in Bilal's. (Writing steps with a letter-number and simplifying, pages 135 and 136.)

Question 2. A three-row number pyramid has 7 and 10 as the two outer numbers of its bottom row, and its middle bottom number can be any whole number. (a) Which of 40, 41, 52 and 53 can be the top number? (b) What is the smallest top number this pyramid can have?

Answer: (a) only 41 and 53; (b) 17. For a bottom row a, b, c the top is a + 2b + c, so here it is 7 + 2b + 10 = 17 + 2b. (a) 2b is even and 17 is odd, so the top is always odd: 41 and 53 are possible, 40 and 52 are not. (b) The top is smallest when b is smallest, b = 0, which gives 17. (The top of a three-row pyramid, a + 2b + c, page 140.)

Question 3. Take any four consecutive whole numbers. Show that the product of the middle two is always 2 more than the product of the outer two.

Answer: (n + 1)(n + 2) − n(n + 3) = 2 for every n. Call the numbers n, n + 1, n + 2 and n + 3. The outer product is n(n + 3) = n² + 3n. The middle product is (n + 1)(n + 2) = n² + 2n + n + 2 = n² + 3n + 2. The difference is 2, whatever n is. For example, with 5, 6, 7, 8: 6 × 7 = 42 and 5 × 8 = 40. (Writing numbers with a letter-number and simplifying, pages 135 to 141.)

Digits and numbers

Question 4. Find every two-digit number that is equal to 4 times the sum of its digits.

Answer: 12, 24, 36 and 48. Write the number as 10a + b, where a is the tens digit and b the ones digit. The condition is 10a + b = 4(a + b) = 4a + 4b, so 6a = 3b, that is, b = 2a. Since b is a single digit, a can only be 1, 2, 3 or 4, giving 12, 24, 36 and 48. Check 36: 3 + 6 = 9 and 4 × 9 = 36. (Writing a two-digit number as 10a + b, page 145.)

Question 5. Show that the sum of any five consecutive whole numbers is 5 times the middle one. Which of 335, 342 and 1,000 can be the sum of five consecutive whole numbers?

Answer: the sum is 5n; 335 and 1,000 can, 342 cannot. Let the middle number be n. The five numbers are n − 2, n − 1, n, n + 1 and n + 2, and their sum is (n − 2) + (n − 1) + n + (n + 1) + (n + 2) = 5n. So the sum is always a multiple of 5. 335 = 5 × 67 and 1,000 = 5 × 200 are multiples of 5, so each can be such a sum (around 67, and around 200); 342 is not a multiple of 5, so it cannot. (Writing numbers with a letter-number and simplifying, pages 135 to 141.)

Question 6. Taxi Plan A charges ₹90 plus ₹11 for every kilometre. Plan B charges ₹36 plus ₹14 for every kilometre. (a) What does Plan A charge for 26 km? (b) For what distance do the two plans charge the same, and how much is that? (c) Which plan is cheaper for 30 km?

Answer: (a) ₹376; (b) 18 km, ₹288 on both; (c) Plan A. (a) 90 + 11 × 26 = 90 + 286 = ₹376. (b) Let the distance be k km. Equal fares mean 90 + 11k = 36 + 14k. Subtract 11k from both sides: 90 = 36 + 3k. Subtract 36: 54 = 3k, so k = 18 km. Each plan then charges 90 + 11 × 18 = 36 + 14 × 18 = ₹288. (c) For 30 km, Plan A charges 90 + 330 = ₹420 and Plan B charges 36 + 420 = ₹456, so Plan A is cheaper. It has the higher fixed charge but the lower rate per kilometre, so it wins on long trips and loses on short ones. (Forming an equation and solving it step by step, page 141; algebra to model a situation, page 147.)

Question 7. Which two-digit numbers give exactly 63 when you subtract the sum of their digits from them? Find all of them.

Answer: all ten numbers from 70 to 79. Write the number as 10a + b. Subtracting the digit sum gives 10a + b − (a + b) = 9a, which does not depend on b at all. So 9a = 63, a = 7, and b can be any digit: 70, 71, …, 79. Check: 74 − (7 + 4) = 63 and 79 − 16 = 63. (Writing a two-digit number as 10a + b, page 145.)

Question 8. In a two-digit number, the tens digit is 3 more than the ones digit. The number and the number made by reversing its digits add up to 99. Find the number, using a letter-number for the ones digit.

Answer: 63. Let the ones digit be u. Then the tens digit is u + 3, and the number is 10(u + 3) + u = 11u + 30. The reversed number has u as its tens digit and u + 3 as its ones digit, so it is 10u + (u + 3) = 11u + 3. Their sum is (11u + 30) + (11u + 3) = 22u + 33. Setting 22u + 33 = 99 gives 22u = 66 and u = 3. The tens digit is 3 + 3 = 6, so the number is 63. Check: 63 + 36 = 99. (A two-digit number and its reversal, page 145; solving for a letter-number, page 141.)

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Sources

All opened and read on 30 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 134.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.