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Algebra Play Class 8 Maths Worksheet with Answers Chapter 6

Updated:7 Mins Read

Ganita Prakash Part-II, Grade 8, Textbook of Mathematics – Chapter 6 in NCERT book Ganita Prakash Part-II, Algebra Play is one of the most important chapters in class 8. In this chapter’s worksheet, you are going to solve problems related to the below topics –

  • Number trick patterns
  • Algebra using variables
  • Pyramid sum puzzles
  • Calendar grid algebra
  • Logic and equations

The questions in this worksheet is broken down into 4 parts – Basic, Standard, Advance, and HOTS. The answers is also there at the end.

Class 8 Maths Worksheet – Chapter 6: Algebra Play

Basic

  1. Think of a number trick:
    Think of a number. Triple it. Add 6. Divide by 3. Subtract the original number.
    What answer do you always get?
  2. Modify the previous trick so that the final answer is always 3.
    (Write the new steps.)
  3. Date trick (decode the date):
    Someone follows the date steps from the chapter and tells you the final answer is 1269.
    What date did they think of? (Write as DD/MM)
  4. Number pyramid:
    In a 3-row pyramid, each box is the sum of the two boxes directly below it.
    If the bottom row is 3, 4, 3, what number is at the top?
  5. Calendar magic (2×2 grid):
    In a calendar, a 2×2 grid has sum 52.
    Find the four numbers in the grid.
  6. Reverse-and-subtract trick:
    Start with 47. Reverse to get 74. Subtract the smaller from the larger. Divide by 9.
    What quotient do you get?

Standard

  1. Always-5 trick (design):
    Create a “think of a number” trick that always ends in 5 using exactly these operations:
    Multiply → Add → Divide → Subtract original number.
    Write your steps clearly.
  2. Date trick (decode):
    Final answer reported is 296.
    Find the date (DD/MM).
  3. Number pyramid (missing middle):
    Top is 50. Bottom row is 4, x, 6.
    Find x and complete the pyramid.
  4. Calendar magic (2×2 grid):
    The sum of a 2×2 calendar grid is 68.
    Find the four numbers.
  5. Algebra grid (shapes):
    Let square = s, triangle = t, circle = c.
    Given:

    • s + t + c = 27
    • 2s + c = 21
    • t + 2c = 18

    Find s, t, and c.

  6. Largest product:
    Use the digits 3, 5, 9 exactly once in __ __ × __.
    Find the largest possible product.

Advance

  1. Cyclic digits (divisible by 37):
    Take 258. Form 258, 582, and 825 and add them.
    Find the sum and check if it is divisible by 37.
  2. abcabc trick:
    Take abc = 246. Form abcabc = 246246.
    Divide it by 7, then by 11, then by 13. What do you get?
  3. Three shrines, three ponds:
    A person starts with some flowers.
    At each pond, the flowers double. After pond 1 he places some flowers in shrine 1.
    After pond 2 he places the same number in shrine 2.
    After pond 3 he places all remaining flowers in shrine 3.
    If each shrine gets the same number of flowers, find:

    • How many flowers did he start with?
    • How many flowers in each shrine?
  4. Heads and legs:
    A farm has horses and hens. Total heads = 55, total legs = 150.
    Find the number of horses and hens.
  5. Mother-daughter ages:
    A mother is 5 times her daughter’s age.
    In 6 years, the mother will be 3 times her daughter’s age.
    Find the daughter’s present age.
  6. Dosa cart profit:
    Rent is ₹5000 per day and the cost of making one dosa is ₹10.

    • If 100 dosas are sold, what should be the selling price per dosa to make profit ₹2000?
    • If customers pay only ₹50 per dosa, how many dosas must be sold to make profit ₹2000?

HOTS

  1. Calendar formula:
    In a 2×2 calendar grid, let the top-left number be a.
    The grid is:
    a, a+1
    a+7, a+8
    Show that the sum is 4a + 16.
    If the sum is 92, find the four numbers.
  2. Largest product (general rule):
    Digits p, q, r satisfy p < q < r.
    You must place them in __ __ × __.
    Which arrangement gives the largest product? (Write the arrangement and one-line reason.)
  3. Reverse-and-add trick:
    Take any 2-digit number ab (a ≠ b). Reverse it to ba and add:
    (10a + b) + (10b + a)
    Show the sum is always divisible by 11.
  4. Fraction pattern:
    Evaluate:
    1/3, (1+3)/(5+7), (1+3+5)/(7+9+11)
    What do you observe? Explain in 2–3 lines why it happens.
  5. Genie deal:
    Karim goes around a tree 3 times.
    Each time, his coins double, and then he must give the genie 8 coins.
    After the third round, he has exactly 8 coins left (and he still owes 8).
    How many coins did Karim have at the start?
  6. Invent your own trick:
    Create a “think of a number” trick that always ends in 7.
    Write the steps and also write a short algebra proof using x.

Answer Key

Basic – Answers

  1. Ans: 2
    Hint: Let the number be x: 3x → 3x+6 → (3x+6)/3 = x+2 → (x+2)−x = 2.
  2. Ans (one example): Triple it → Add 9 → Divide by 3 → Subtract original → always 3
    Hint: 3x+9 → (3x+9)/3 = x+3 → (x+3)−x = 3.
  3. Ans: 04/11 (4th November)
    Hint: Subtract 165: 1269 − 165 = 1104 = 100M + D ⇒ M=11, D=04.
  4. Ans: 14
    Hint: Middle row: 3+4=7 and 4+3=7, top: 7+7=14.
  5. Ans: 9, 10, 16, 17
    Hint: Sum = 4a+16. So 4a+16=52 ⇒ a=9.
  6. Ans: 3
    Hint: 74−47=27, 27/9=3.

Standard – Answers

  1. Ans (one example):
    Multiply by 4 → Add 20 → Divide by 4 → Subtract original → always 5
    Hint: 4x+20 → (4x+20)/4 = x+5 → (x+5)−x = 5.
  2. Ans: 31/01 (31st January)
    Hint: 296 − 165 = 131 = 100M + D ⇒ M=1, D=31.
  3. Ans: x = 20
    Pyramid: Middle row: 24 and 26; Top: 50
    Hint: Top = (4+x) + (x+6) = 2x+10 = 50.
  4. Ans: 13, 14, 20, 21
    Hint: 4a+16=68 ⇒ a=13.
  5. Ans: s = 10, t = 16, c = 1
    Hint: From 2s+c=21 ⇒ c=21−2s. Substitute into others.
  6. Ans: 53 × 9 = 477
    Hint: Put the largest digit as the multiplier (9), and arrange the other two as 53.

Advance – Answers

  1. Ans: 258+582+825 = 1665, and 1665 ÷ 37 = 45
    Hint: Check 37×45 = 1665.
  2. Ans: 246
    Hint: 246246 = 1001×246 and 1001 = 7×11×13.
  3. Ans: Start with 7 flowers, each shrine gets 8
    Hint: Try smallest number that makes equal sharing possible; check by working backward.
  4. Ans: Horses = 20, Hens = 35
    Hint: 4h + 2(55−h) = 150.
  5. Ans: Daughter = 6 years
    Hint: 5d+6 = 3(d+6).
  6. Ans:

    • Selling price = ₹80
    • Required dosas = 175

    Hint: Profit = Revenue − (Rent + Making cost).

HOTS – Answers

  1. Ans: Sum = 4a+16.
    If sum=92: 4a+16=92 ⇒ a=19.
    Grid: 19, 20, 26, 27
  2. Ans: Largest product is qp × r
    Reason: Use the largest digit as multiplier and make the 2-digit number as large as possible.
  3. Ans: (10a+b)+(10b+a)=11(a+b), so divisible by 11
    Hint: Factor 11 out.
  4. Ans: All are 1/3
    Hint: (1+3+…+(2n−1)) = n² and (5+7+… up to n terms) = 3n², so ratio = n²/(3n²)=1/3.
  5. Ans: 7 coins
    Hint: After 3 rounds: start N.
    After round1: 2N−8
    After round2: 2(2N−8)−8 = 4N−24
    After round3: 2(4N−24) = 8N−48 equals 8 ⇒ N=7.
  6. Ans (one example):
    Multiply by 5 → Add 35 → Divide by 5 → Subtract original → always 7
    Proof: Start x → 5x → 5x+35 → (5x+35)/5 = x+7 → (x+7)−x = 7.

Worksheet From Other Chapters

Ganita Prakash Part-I

Ganita Prakash Part-II

Amit, a BE in Mechanical Engineering, is a math enthusiast dedicated to making math fun and accessible for kids in classes 1 to 10. With a knack for simplifying complex concepts, Amit offers easy-to-understand solutions, fostering a love for math in young minds across India.

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