NCERT Solutions Class 6th Maths Chapter – 11 Algebra Exercise – 11.5

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
Solution: An equation with variable x

(b) (t – 7) > 5
Solution: An inequality equation

(c) 4/2 = 2
Solution: No, it’s a numerical equation

(d) (7 x 3) – 19 = 8
Solution: No, it’s a numerical equation

(e) 5 × 4 – 8 = 2x
Solution: An equation with variable x

(f) x – 2 = 0
Solution: An equation with variable x

(g) 2m < 30
Solution: An inequality equation

(h) 2n + 1 = 11
Solution: An equation with variable n

(i) 7 = (11 × 5) – (12 × 4)
Solution: No, it’s a numerical equation

(j) 7 = (11 × 2) + p
Solution: An equation with variable p

(k) 20 = 5y
Solution: An equation with variable y

(l) 3q/2 < 5 
Solution: An inequality equation

(m) z + 12 > 24
Solution: An inequality equation

(n) 20 – (10 – 5) = 3 × 5
Solution: No, it’s a numerical equation

(o) 7 – x = 5
Solution: An equation with variable x

Solution:

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)

Solution: 5m = 60
m = 12 is a solution for this equation because for m = 12,
5m = 5 × 12
= 60
∴ Equation satisfied
m = 10 is not a solution for this equation because for m = 10,
5m = 5 × 10
= 50 and not 60
m = 5 is not a solution for this equation because for m = 5,
5m = 5 × 5
= 25 and not 60
m = 15 is not a solution for this equation because for m = 15,
5m = 5 × 15
= 75 and not 60

(b) n + 12 = 20 (12, 8, 20, 0)

Solution: n + 12 = 20
n = 8 is a solution for this equation because for n = 8,
n + 12 = 8 + 12
= 20
∴ Equation satisfied
n = 12 is not a solution for this equation because for n = 12,
n + 12 = 12 + 12
= 24 and not 20
n = 20 is not a solution for this equation because for n = 20,
n + 12 = 20 + 12
= 32 and not 20
n = 0 is not a solution for this equation because for n = 0,
n + 12 = 0 + 12
= 12 and not 20

(c) p – 5 = 5 (0, 10, 5, -5)

Solution: p – 5 = 5
p = 10 is a solution for this equation because for p = 10,
p – 5 = 10 – 5
= 5
∴ Equation satisfied
p = 0 is not a solution for this equation because for p = 0,
p – 5 = 0 – 5
= -5 and not 5
p = 5 is not a solution for this equation because for p = 5,
p – 5 = 5 – 5
= 0 and not 5
p = -5 is not a solution for this equation because for p = -5,
p – 5 = -5 – 5
= – 10 and not 5

(d) q/2 = 7 (7, 2, 10, 14)

Solution: q / 2 = 7
q = 14 is a solution for this equation because for q = 14,
q / 2 = 14 / 2
= 7
∴ Equation satisfied
q = 7 is not a solution for this equation because for q = 7,
q / 2 = 7 / 2 and not 7
q = 2 is not a solution for this equation because for q = 2,
q / 2 = 2 / 2
= 1 and not 7
q = 10 is not a solution for this equation because for q = 10,
q / 2 = 10 / 2
= 5 and not 7

(e) r – 4 = 0 (4, -4, 8, 0)

Solution: r – 4 = 0
r = 4 is a solution for this equation because for r = 4,
r – 4 = 4 – 4
= 0
∴ Equation satisfied
r = -4 is not a solution for this equation because for r = – 4,
r – 4 = – 4 – 4
= -8 and not 0
r = 8 is not a solution for this equation because for r = 8,
r – 4 = 8 – 4
= 4 and not 0
r = 0 is not a solution for this equation because for r = 0,
r – 4 = 0 – 4
= – 4 and not 0

(f) x + 4 = 2 (-2, 0, 2, 4)

Solution: x + 4 = 2
x = -2 is a solution for this equation because for x = -2,
x + 4 = – 2 + 4
= 2
∴ Equation satisfied
x = 0 is not solution for this equation because for x = 0,
x + 4 = 0 + 4
= 4 and not 2
x = 2 is not a solution for this equation because for x = 2,
x + 4 = 2 + 4
= 6 and not 2
x = 4 is not a solution for this equation because for x = 4,
x + 4 = 4 + 4
= 8 and not 2

Question 4. (a) Complete the table and by inspection of the table find the solution to the equation m + 10 = 16.

(b) Complete the table and by inspection of the table, find the solution to the equation 5t = 35

(c) Complete the table and find the solution of the equation z / 3 = 4 using the table.

z	8	9	10	11	12	13	14	15	16	—	—	—	—
z / 3		3		—	—	—	—	—	—	—	—	—	—

(d) Complete the table and find the solution to the equation m – 7 = 3.

Solution:

(a) For m + 10, the table is represented as below

Now, by inspection we may conclude that the solution of the above equation since, for m = 6,
m + 10 = 6 + 10 = 16

(b) For 5t, the table is represented as below

Now, by inspection we may conclude that t = 7 is the solution of the above equation since, for t = 7,
5t = 5 × 7 = 35

(c) For z / 3, the table is represented as below

z	z / 3
8	8 / 3 =
9	9 / 3 = 3
10	10 / 3 =
11	11 / 3 =
12	12 / 3 = 4
13	13 / 3 =
14	14 / 3 =
15	15 / 3 = 5
16	16 / 3 =

Now, by inspection we may conclude that z = 12 is the solution of the above equation since for z = 12,
z / 3 = 12/3 = 4

(d) For m – 7, the table is represented as below

Now, by inspection we may conclude that m = 10 is the solution of the above equation since, for m = 10,
m – 7 = 10 – 7 = 3

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!

Solution:
According to the condition,
I + 12 = 34 or x + 12 = 34
∴ By inspection, we have
22 + 12 = 34
So, I am 22.

(ii) For each day of the week
Make an upcount from me
If you make no mistake
you will get twenty three!

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

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