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About Algebra — Class 6 Olympiad

Introduce variables, form expressions and equations, and solve age/coin/number puzzles algebraically. This topic is part of the Olympiad Class 6 mathematics syllabus (chapter: Module 6). On this page you can practice 53 questions across three difficulty levels — 20 easy, 20 medium, and 13 hard — each with a visual step-by-step solution, plus a timed 30-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Algebra — solved examples for Class 6 Olympiad

Example 1easy

Rohan has a certain number of marbles, which we represent by 'm'. His friend gives him 7 more marbles. Which algebraic expression correctly shows the total number of marbles Rohan has now?
  1. A)m - 7
  2. B)7 × m
  3. C)m + 7
  4. D)m / 7

Step-by-step solution

  1. Let the initial number of marbles Rohan has be 'm'.
  2. His friend gives him 7 more marbles, which means we add 7 to the initial number.
  3. Therefore, the total number of marbles Rohan has now is represented by the expression m + 7.

Answer: m + 7

Example 2medium

The cost of a pencil is 'p' rupees. The cost of a pen is 3 rupees more than twice the cost of a pencil. A student buys 4 pencils and 2 pens. Which expression correctly represents the total cost incurred by the student?
  1. A)(6p + 6) rupees
  2. B)(8p + 6) rupees
  3. C)(4p + 3) rupees
  4. D)(10p + 3) rupees

Step-by-step solution

  1. Cost of a pencil = p rupees.
  2. Cost of a pen = (2 × p) + 3 = (2p + 3) rupees.
  3. Cost of 4 pencils = 4 × p = 4p rupees.
  4. Cost of 2 pens = 2 × (2p + 3) = 4p + 6 rupees.
  5. Total cost = Cost of 4 pencils + Cost of 2 pens = 4p + (4p + 6) = (8p + 6) rupees.

Answer: (6p + 6) rupees

Example 3hard

A baker bakes `x` loaves of bread. Each loaf requires `y` grams of flour. He uses `1/5` of the total flour for cakes and `1/4` of the *remaining* flour for cookies. How much flour (in grams) is left?
  1. A)(xy / 5)
  2. B)(2xy / 5)
  3. C)(4xy / 5)
  4. D)(3xy / 5)

Step-by-step solution

  1. Total flour = `x × y = xy` grams.
  2. Flour used for cakes = `(1/5) × xy = xy/5` grams.
  3. Remaining flour after cakes = `xy - xy/5 = 4xy/5` grams.
  4. Flour used for cookies = `(1/4) × (4xy/5) = xy/5` grams.
  5. Flour left = (Remaining flour after cakes) - (Flour for cookies) = `(4xy/5) - (xy/5) = 3xy/5` grams.

Answer: (3xy / 5)

Practice questions on Algebra

  1. Q1.easy

    A number 'p' is first multiplied by 5, and then 8 is subtracted from the result. Which algebraic expression correctly represents this sequence of operations?
    1. A)p × 5 - 8
    2. B)8 - 5p
    3. C)(p - 8) × 5
    4. D)5 + p - 8
    Show answer

    Answer: p × 5 - 8

    Hint: Remember the order of operations. The multiplication happens first, and then the subtraction.

  2. Q2.easy

    If the value of 'a' is 6 and the value of 'b' is 2, what is the value of the expression 4a - 3b + 1?
    1. A)17
    2. B)19
    3. C)23
    4. D)20
    Show answer

    Answer: 19

    Hint: Substitute the given values of 'a' and 'b' into the expression and then perform the arithmetic operations carefully.

  3. Q3.easy

    Which of the following statements represents an equation?
    1. A)3x + 5
    2. B)y - 12 > 7
    3. C)4p = 20
    4. D)2(a + b)
    Show answer

    Answer: 4p = 20

    Hint: An equation always involves an equality sign (=), showing that two expressions have the same value.

  4. Q4.medium

    Consider a mysterious number. If you multiply it by 4, then subtract 12, and then divide the entire result by 2, you get a number that is 5 less than the original mysterious number. What is the mysterious number?
    1. A)7
    2. B)9
    3. C)11
    4. D)13
    Show answer

    Answer: 9

    Hint: Let the mysterious number be 'x'. Form an equation based on the given operations, with 'x' appearing on both sides of the equation.

  5. Q5.medium

    Rohan is 'x' years old. His sister, Priya, is 3 years younger than him. Their father is 5 years more than twice Rohan's age. If the sum of Rohan's and Priya's ages is 27, how old is their father?
    1. A)41 years
    2. B)47 years
    3. C)53 years
    4. D)59 years
    Show answer

    Answer: 47 years

    Hint: First, use the information about Rohan's and Priya's ages to find the value of 'x'. Then, use 'x' to calculate the father's age.

  6. Q6.medium

    If 5 multiplied by a number 'm' and then subtracted by 7 gives a result of 18, what is the value of (m + 3) × (m - 2)?
    1. A)42
    2. B)48
    3. C)55
    4. D)60
    Show answer

    Answer: 42

    Hint: First, set up an equation to find the value of 'm'. Once 'm' is known, substitute it into the expression (m + 3) × (m - 2) to find its value.

  7. Q7.hard

    A sequence of figures is formed by arranging unit squares. Figure 1 has 1 square. Figure 2 has 5 squares. Figure 3 has 13 squares. Following this pattern, how many squares will be there in Figure `n`?
    1. A)n² + 1
    2. B)2n² - 2n + 1
    3. C)4n - 3
    4. D)n³ - n + 1
    Show answer

    Answer: 2n² - 2n + 1

    Hint: Analyze the number of squares in each figure: 1, 5, 13. Calculate the differences between consecutive terms. If the first differences are not constant, check the second differences. This will reveal the nature of the algebraic rule.

  8. Q8.hard

    If `P` is a positive integer such that `P + Q = 10` and `Q` is also a positive integer, which of the following statements about `Q` must be true?
    1. A)`Q` is always greater than `P`.
    2. B)`Q` is always an even number.
    3. C)`Q` can be any positive integer less than 10.
    4. D)`Q` must be greater than 5.
    Show answer

    Answer: `Q` can be any positive integer less than 10.

    Hint: Analyze the constraints on `P` and `Q`. Since both are positive integers, they have minimum values. Use `P + Q = 10` to find the possible range of values for `Q`.

  9. Q9.hard

    The sum of three consecutive odd numbers is 189. If the smallest number is increased by 10 and the largest number is decreased by 5, what is the product of the new smallest and new largest numbers?
    1. A)3850
    2. B)3900
    3. C)4000
    4. D)4050
    Show answer

    Answer: 4000

    Hint: Represent the three consecutive odd numbers using a single variable. Remember the pattern for consecutive odd numbers.

These are 9 of the 53 questions available for Algebra. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.