Study MaterialsRD Sharma SolutionsNCERT Solutions For Class 6 Maths Algebra Exercise 11.5

NCERT Solutions For Class 6 Maths Algebra Exercise 11.5

NCERT Solutions For Class 6 Maths Algebra Exercise 11.5

NCERT Solutions For Class 6 Maths Chapter 11 Algebra Ex 11.5

Exercise 11.5

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    Ex 11.5 Class 6 Maths Question 1.
    State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable.
    (a) 17 = x + 7
    (b) (t – 7) > 5
    (c) \(\frac { 4 }{ 2 }\) = 2
    (d) (7 x 3) – 19 = 8
    (e) 5 x 4 – 8 = 2x
    (f) x -2 = 0
    (g) 2m < 30
    (h) 2n + 1 = 11
    (i) 7 = (11 x 5) – (12 x 4)
    (j) 7 = (11 x 2) + p
    (k) 20 = 5y
    (l) \(\frac { 3q }{ 2 }\) < 5 (m) z + 12 > 24
    (n) 20 – (10 – 5) = 3 x 5
    (o) 7 – x = 5
    Solution:
    (a) 17 = x + 7 is an equation with a variable x.
    (b) (t – 7) > 5 is not an equation because it does not have ‘=’ sign.
    (c) \(\frac { 4 }{ 2 }\) = 2 is not an equation because it has no variable.
    (d) (7 x 3) – 19 = 8 is not an equation because it has no variable.
    (e) 5 x 4 – 8 = 2x is an equation with a variable x.
    (f) x – 2 = 0 is an equation with a variable x.
    (g) 2m < 30 is not an equation because it does not have ‘=’ sign.
    (h) 2n + 1 = 11 is an equation with a variable n.
    (i) 7 = (11 x 5) – (12 x 4) is not an equation because it does not have a variable.
    (j) 7 = (11 x 2) + p is an equation with a variable p.
    (k) 20 = 5y is an equation with a variable y.
    (l) \(\frac { 3q }{ 2 }\) < 5 is not an equation because it does not have ‘=’ sign. (m) z + 12 > 24 is not an equation because it does not have ‘=’ sign.
    (n) 20 – (10 – 5) = 3 x 5 is not an equation because it has no variable.
    (o) 7 – x = 5 is an equation with a variable x.

    Ex 11.5 Class 6 Maths Question 2.
    Complete the entries in the third column of the table.

    S. No. Equation Value of variable Equations satisfied Yes /No
    (a) 10y = 80 y = 10
    (b) 10y = 80 y = 8
    (c) 10y = 80 y = 5
    (d) 4l = 20 l = 20
    (e) 4l = 20 l = 80
    (f) 4l = 20 l = 5
    (g) b + 5 = 9 b = 5
    (h) b + 5 = 9 b = 9
    (i) b + 5 = 9 b = 4
    (J) h – 8 = 5 h = 13
    (k) h – 8 = 5 h = 8
    (l) h – 8 = 5 h = 0
    (m) P + 3 = 1 p = 3
    (n) p + 3 = 1 p = 1
    (o) p + 3 = 1 p = 0
    (P) p + 3 = 1 p = -1
    (q) p + 3 = 1 p = -2

    Solution:

    S. No. Equation Value of variable Equations satisfied Yes /No
    (a) 10y = 80 y = 10 No
    (b) 10y = 80 y = 8 Yes
    (c) 10y = 80 y = 5 No
    (d) 4l = 20 l = 20 No
    (e) 4l = 20 l = 80 No
    (f) 4l = 20 l = 5 Yes
    (g) b + 5 = 9 b = 5 No
    (h) b + 5 = 9 b = 9 No
    (i) b + 5 = 9 b = 4 Yes
    (J) h – 8 = 5 h = 13 Yes
    (k) h – 8 = 5 h = 8 No
    (l) h – 8 = 5 h = 0 No
    (m) P + 3 = 1 p = 3 No
    (n) p + 3 = 1 p = 1 No
    (o) p + 3 = 1 p = 0 No
    (P) p + 3 = 1 p = -1 No
    (q) p + 3 = 1 p = -2 Yes

    Ex 11.5 Class 6 Maths Question 3.
    Pick out the solution from the values given in the brackets next to each equation. Show that the other values do not satisfy the equation.
    (а) 5m = 60 (10, 5, 12, 15)
    (b) n + 12 = 20 (12, 8, 20, 0)
    (c) p – 5 = 5 (0, 10, 5, -5)
    (d) \(\frac { q }{ 2 }\) = 7 (7, 2, 10, 14)
    (e) r – 4 = 0 (4, -4, 8, 0)
    (f) x + 4 = 2 (-2, 0, 2, 4)
    Solution:
    (a) For m = 10, LHS = 5 x 10 = 50, RHS = 60
    Here, LHS ≠ RHS
    ∴ m = 10 is not the solution of the equation
    For m = 5, LHS = 5×5 = 25, RHS = 60
    Here, LHS ≠ RHS
    ∴ m = 5 is not the solution of the equation
    For m = 12, LHS = 5 x 12 = 60, RHS = 60
    Here, LHS = RHS
    ∴ m = 12 is the solution of the equation
    For m = 15 LHS = 5 x 15 = 75, RHS = 60
    Here, LHS ≠ RHS
    ∴ m = 15 is not the solution of the equation

    (b) n + 12 = 20 (12, 8, 20, 0)
    For n = 12, LHS = 12 + 12 = 24, RHS = 20
    Here, LHS ≠ RHS
    ∴ n = 12 is not the solution of the equation
    For n = 8, LHS = 8 + 12 = 20, RHS = 20
    Here, LHS = RHS
    ∴ n = 8 is the solution of the equation
    For n = 20, LHS = 20 + 12 = 32, RHS = 20
    Here, LHS ≠ RHS
    ∴ n = 20 is not the solution of the equation
    For n = 0, LHS = 0 + 12 – 12, RHS = 20
    Here, LHS ≠ RHS
    ∴ n= 0 is not the solution of the equation

    (c) p – 5 = 5 (0, 10, 5, -5)
    For p = 0, LHS = 0 – 5 = -5, RHS = 5
    Here, LHS ≠ RHS
    ∴ p = 0 is not the solution of the equation
    For p = 10, LHS = 10 – 5 = 5, RHS = 5
    Here, LHS = RHS
    ∴ p = 10 is the solution of the equation
    For p = 5, LHS = 5-5-0, RHS = 5
    Here LHS ≠ RHS
    ∴ p = 5 is not the solution of the equation
    For p = 5, LHS = 5 – 5 = 0, RHS = 5
    Here, LHS ≠ RHS
    ∴ p = -5 is not the solution of the equation

    (d) \(\frac { q }{ 2 }\) = 7 (7, 2, 10, 14)
    For q = 7, LHS = \(\frac { 7 }{ 2 }\) , RHS = 7
    Here LHS ≠ RHS
    ∴ q = 7 is not the solution of the equation
    For q = 2, LHS = \(\frac { 2 }{ 2 }\) = 1, RHS = 7
    Here, LHS ≠ RHS
    ∴ q = 2 is not the solution of the equation
    For q = 10, LHS = \(\frac { 10 }{ 2 }\) = 5, RHS = 7
    Here, LHS ≠ RHS
    For q = 14, LHS = \(\frac { 14 }{ 2 }\) = 7, RHS = 7
    Here, LHS = RHS
    ∴ q = 14 is the solution of the equation

    (e) r – 4 = 0 (4, -4, 8, 0)
    For r = 4, LHS = 4 – 4 = 0, RHS = 0
    Here, LHS = RHS
    ∴ r = 4 is the solution of the equation
    For r = -4, LHS = -4 – 4 = -8, RHS = 0
    Here, LHS ≠ RHS
    ∴ r = -4 is not the solution of the equation
    For r = 8, LHS = 8 – 4 = 4, RHS = 0
    Here, LHS ≠ RHS
    For r = 8 is not the solution of the equation
    For r = 0, LHS = 0 – 4 = – 4, RHS = 0
    Here, LHS ≠ RHS
    ∴ r = 0 is not the solution of the equation

    (f) x + 4 = 2 (-2, 0, 2, 4)
    For x = -2, LHS = -2 + 4 = 2, RHS = 2
    Here, LHS – RHS
    ∴ x = -2 is the solution of the equation
    For x = 0, LHS = 0 + 4 – 4, RHS = 2
    Here, LHS ≠ RHS
    ∴ x = 0 is not the solution of the equation
    For x = – 2, LHS = -2 + 4 – 6, RHS = 2
    Here, LHS ≠ RHS
    ∴ x = 2 is not the solution of the equation
    For r = 4, LHS = 4 + 4 = 8, RHS = 2
    Here, LHS ≠ RHS
    ∴ x = 4 is not the solution of the equation

    Ex 11.5 Class 6 Maths Question 4.
    (a) Complete the table and by inspection of the table find the solution to the equation m + 10 = 6
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    (b) Complete the table and by inspection of the table find the solution to the equation 51 – 35
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    (c) Complete the table and find the solution of the equation g = 4 using the table.
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    (d) Complete the table and find the solution to the equation m – 7 = 3
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    Solution:
    (a) By inspections, we have
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    So, m – 6 is the solution of the equation.

    (b) Given that 5t = 35
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    So, t = 7 is the solution of the equation.

    (c) Given that \(\frac { z }{ 3 }\) = 35
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    So, z = 12 is the solution of the equation.

    (d) Given that m – 7 = 3
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra
    So, m = 10 is the solution of the equation.

    Ex 11.5 Class 6 Maths Question 5.
    Solve the following riddles, you may yourself construct such riddles. Who am I?
    (i) Go round a square
    Counting every corner
    Thrice and no more!
    Add the count to me
    To get exactly thirty four!
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra

    (ii) For each day of the week
    Make an upcount from me
    If you make no mistake
    you will get twenty three!
    NCERT Solutions For Class 6 Maths Chapter 11 Algebra

    (iii) I am a special number
    Take away from me a six!
    A whole cricket team
    You will still be able to fix!

    (iv) Tell me who I am
    I shall give you a pretty clue!
    you will get me back
    If you take me out of twenty two!
    Solution:
    (i) According to the condition,
    I + 12 = 34 or x + 12 = 34
    ∴ By inspection, we have
    22 + 12 = 34
    So, I am 22.

    (ii) Let I am ‘x’.
    We know that there are 7 days in a week.
    ∴ upcounting from x for 7, the sum = 23
    By inspections, we have
    16 + 7 = 23
    ∴ x = 16
    Thus I am 16.

    (iii) Let the special number be x and there are 11 players in cricket team.
    ∴ Special Number -6 = 11
    ∴ x – 6 = 11
    By inspection, we get
    17 – 6 = 11
    ∴ x = 17
    Thus I am 17.

    (iv) Suppose I am ‘x’.
    ∴ 22 – I = I
    or 22 – x = x
    By inspection, we have
    22 – 11 = 11
    ∴ x = 11
    Thus I am 11.

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