NCERT Solutions For Class 6 Maths Chapter 11 - Algebra

(a)

From the figure, we observe that two matchsticks are required to make the letter T. Hence, the pattern is 2n

(b)

From the figure, we observe that three matchsticks are required to make the letter Z. Hence, the pattern is 3n

(c)

From the figure, we observe that three matchsticks are required to make the letter U. Hence, the pattern is 3n

(d)

From the figure, we observe that two matchsticks are required to make the letter V. Hence, the pattern is 2n

(e)

From the figure, we observe that 5 matchsticks are required to make the letter E. Hence, the pattern is 5n

(f)

From the figure, we observe that 5 matchsticks are required to make the letter S. Hence, the pattern is 5n

(g)

From the figure, we observe that 6 matchsticks are required to make the letter A. Hence, the pattern is 6n

 

We know that T require only two matchsticks. So, the pattern for the letter T is 2n. Among all the letters given in question 1, only T and V are the letters which require two matchsticks. Hence, (a) and (d).

 

Let n be the number of rows

Number of cadets in a row = 5

Total number of cadets = number of cadets in a row × number of rows

= 5n

 

Let b be the number of boxes

Number of mangoes in a box = 50

Total number of mangoes = number of mangoes in a box × number of boxes

= 50b

 

Let s be the number of students

Pencils given to each student = 5

Total number of pencils = number of pencils given to each student × number of students

= 5s

 

Let t minutes be the flying times

Distance covered in one minute = 1 km

Distance covered in t minutes = Distance covered in one minute × Flying time

= 1 × t

= t km

 

Number of dots in a row = 9

Number of rows = r

Total number of dots in r rows = Number of dots in a row × number of rows

= 9r

Number of dots in 8 rows = 8 × 9

= 72

Number of dots in 10 rows = 10 × 9

= 90

 

Let Radha’s age be x years

Leela’s age = 4 years younger than Radha

= (x – 4) years

 

Number of laddus mother gave = l

Remaining laddus = 5

Total number of laddus = number of laddus given away by mother + number of laddus remaining

= (l + 5) laddus

 

Number of oranges in a small box = x

Number of oranges in two small boxes = 2x

Number of oranges remaining = 10

Number of oranges in large box = number of oranges in two small boxes + number of oranges remained

= 2x + 10

 

(a) We may observe that in the given matchstick pattern, the number of matchsticks are 4, 7, 10 and 13, which is 1 more than thrice the number of squares in the pattern

Therefore, the pattern is 3x + 1, where x is the number of squares

 

(b) We may observe that in the given matchstick pattern, the number of matchsticks are 3, 5, 7 and 9, which is 1 more than twice the number of triangles in the pattern.

Therefore, the pattern is 2x + 1, where x is the number of triangles.

 

Side of equilateral triangle = l

Perimeter = l + l + l

= 3l

 

Side of a regular hexagon = l

Perimeter = l + l + l + l + l + 1

= 6l

 

Length of an edge of the cube = l

Number of edges = 12

Total length of the edges = Number of edges × Length of an edge

=12l

 

Diameter = AB

= AC + CB

= r + r

= 2r

Hence, the diameter of the circle in terms of its radius is 2r.

 

For any three whole numbers a, b and c,

(a + b) + c = a + (b + c)

(a) (t + 4), (t – 4), 4t, (t / 4), (4 / t), (4 – t), (4 + t) are the expressions using t and 4

(b) 2y + 7, 2y – 7, 7y + 2,… are the expression using y, 2 and 7

Some of the expressions formed by 5, 7 and 8 are as follows

5 × (8 – 7)

5 × (8 + 7)

(8 + 5) × 7

(8 – 5) × 7

(7 + 5) × 8

(7 – 5) × 8

 

(c) and (d) are the expressions with numbers only.

 

(a) 7 is added to p is (p + 7)

(b) 7 subtracted from p is (p – 7)

(c) p multiplied by 7 is (7p)

(d) p divided by 7 is (p / 7)

(e) 7 subtracted from –m is (-m – 7)

(f) –p multiplied by 5 is (-5p)

(g) –p divided by 5 is (–p / 5)

(h) p multiplied by -5 is (-5p)

 

(a) 11 added to 2m is (2m + 11)

(b) 11 subtracted from 2m is (2m – 11)

(c) 5 times y to which 3 is added is (5y + 3)

(d) 5 times y from which 3 is subtracted is (5y – 3)

(e) y is multiplied by -8 is (-8y)

(f) y is multiplied by -8 and then 5 is added to the result is (-8y + 5)

(g) y is multiplied by 5 and the result is subtracted from 16 is (16 – 5y)

(h) y is multiplied by -5 and the result is added to 16 is (-5y + 16)

 

(a) z + 1 = 1 is added to z = Addition

z – 1 = 1 is subtracted from z = Subtraction

y + 17 = 17 is added to y = Addition

y – 17 = 17 is subtracted from y = Subtraction

(b) 17y = y is multiplied by 17 = Multiplication

y / 17 = y is divided by 17 = Division

5z = z is multiplied by 5 = Multiplication

(c) 2y + 17 = y is multiplied by 2 and 17 is added to the result = Multiplication and addition

2y – 17 = y is multiplied by 2 and 17 is subtracted from the result = Multiplication and subtraction

(d) 7m = m is multiplied by 7 = multiplication

-7m + 3 = m is multiplied by -7 and 3 is added to the result = Multiplication and addition

-7m – 3 = m is multiplied by -7 and 3 is subtracted from the result = Multiplication and subtraction

 

(a) A book costs 3 times the costs of a notebook.

 

(b) Tony’s box contains 8 times the number of marbles on the table

 

(c) Total number of students in the school is 20 times that of our class

 

(d) Jaggu’s uncle is 4 times older than Jaggu, and Jaggu’s aunt is 3 years younger than his uncle

 

(e) The total number of dots is 5 times the number of rows

 

(a) (x – 2) represents the person whose age is (x – 2) years, and he is 2 years younger than Munnu

(x + 4) represents the person whose age is (x + 4) years, and he is 4 years older than Munnu

(3x + 7) represents the person whose age is (3x + 7) years, elder to Munnu and his age is 7 years more than three times the age of Munnu

 

(b) In Future

After n years since now, Sara’s age will be (y + n) years

In past

n years ago, Sara’s age was (y – n) years

(y + 7) represents the person whose age is (y + 7) years and is 7 years older than Sara

(y – 3) represents the person whose age is (y – 3) years and is 3 years younger than Sara

represents the person whose age is years and is years older than Sara

represents the person whose age is years and is years younger than Sara

 

(c) 2n shows the number of students who like either football or some other game like tennis, whereas n / 2 shows the number of students who like tennis out of the total number of students who like football.

 

(a)

 (i) Sarita’s age after 5 years from now = Sarita’s present age + 5

= (y + 5) years

(ii) Sarita’s age 3 years back = Sarita’s present age – 3

= (y – 3) years

(iii) Grandfather’s age = 6 × Sarita’s present age

= 6y years

(iv) Grandmother’s age = granfather’s present age – 2

= (6y -2) years

(v) Father’s age = 5 + 3 × Sarita’s present age

= (5 + 3y) years

 

(b) Length = 3 × Breadth – 4

l = (3b – 4) metres

 

(c) Length = 5 × Breadth

l = 5h cm

Breadth = 5 × length – 10

b = (5h – 10) cm

 

(d) The step at which Beena is = (step at which Meena is) + 8

= (s + 8)

The step at which Leena is = (step at which Meena is) – 7

= (s – 7)

Total steps = 4 × (step at which Meena is) – 10

= (4s – 10)

 

(e) Speed = v km / hr

Distance travelled in 5 hours = 5 × v

= 5v km

Total distance travelled between Daspur and Beespur = (5v + 20) km

 

(a) An equation with variable x

(b) An inequality equation

(c) No, it’s a numerical equation

(d) No, it’s a numerical equation

(e) An equation with variable x

(f) An equation with variable x

(g) An inequality equation

(h) An equation with variable n

(i) No, it’s a numerical equation

(j) An equation with variable p

(k) An equation with variable y

(l) An inequality equation

(m) An inequality equation

(n) No, it’s a numerical equation

(o) An equation with variable x

 

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

 

Now, by inspection, we may conclude that m = 6 is 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:

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

 

(i) There are 4 corners in a square.

Thrice the number of corners in the square = 3 × 4 = 12

When 12 is added to the number, it becomes 34

So, the number will be the difference of 34 and 12

34 – 12 = 22

(ii) The result was 23 when the old number was up counted on Sunday

The result was 22 when the old number was up counted on Saturday

The result was 21 when the old number was up counted on Friday

The result was 20 when the old number was up counted on Thursday

The result was 19 when the old number was up counted on Wednesday

The result was 18 when the old number was up counted on Tuesday

The result was 17 when the old number was up counted on Monday

`Hence, the number taken at starting was 17 – 1 = 16

(iii) There are 11 players in a cricket team

If 6 is subtracted from a required number, it will be 11

11 + 6 = 17

Hence, the number is 17

(iv) The required number is such that if it is subtracted from 22, the result is the number itself.

The number is 11 because if it is subtracted from 22, the result will be 11 only.

(a) 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

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

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

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

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

x = -2 is a solution for this equation because for x = -2,

x + 4 = – 2 + 4

= 2

∴ Equation satisfied

x = 0 is not a 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

 

(a) 10y = 80

y = 10 is not a solution for this equation because if y = 10,

10y = 10 × 10

= 100 and not 80

(b) 10y = 80

y = 8 is a solution for this equation because if y = 8,

10y = 10 × 8

= 80

∴ Equation satisfied

(c) 10y = 80

y = 5 is not a solution for this equation because if y = 5,

10y = 10 × 5

= 50 and not 80

(d) 4l = 20

l = 20 is not a solution for this equation because if l = 20,

4l = 4 × 20

= 80 and not 20

(e) 4l = 20

l = 80 is not a solution for this equation because if l = 80,

4l = 4 × 80

= 320 and 20

(f) 4l = 20

l = 5 is a solution for this equation because if l = 5,

4l = 4 × 5

= 20

∴ Equation satisfied

(g) b + 5 = 9

b = 5 is not a solution for this equation because if b = 5,

b + 5 = 5 + 5

= 10 and not 9

(h) b + 5 = 9

b = 9 is not a solution for this equation because if b = 9,

b + 5 = 9 + 5

= 14 and not 9

(i) b + 5 = 9

b = 4 is a solution for this equation because if b = 4,

b + 5 = 4 + 5

= 9

∴ Equation satisfied

(j) h – 8 = 5

h = 13 is a solution for this equation because if h = 13,

h – 8 = 13 – 8

= 5

∴ Equation satisfied

(k) h – 8 = 5

h = 8 is not a solution for this equation because if h = 8,

h – 8 = 8 – 8

= 0 and not 5

(l) h – 8 = 5

h = 0 is not a solution for this equation because if h = 0,

h – 8 = 0 – 8

= – 8 and not 5

(m) p + 3 = 1

p = 3 is not a solution for this equation because if p = 3,

p + 3 = 3 + 3

= 6 and not 1

(n) p + 3 = 1

p = 1 is not a solution for this equation because if p = 1,

p + 3 = 1 + 3

= 4 and not 1

(o) p + 3 = 1

p = 0 is not a solution for this equation because if p = 0,

p + 3 = 0 + 3

= 3 and not 1

(p) p + 3 = 1

p = -1 is not a solution for this equation because if p = – 1,

p + 3 = -1 + 3

= 2 and not 1

(q) p + 3 = 1

p = -2 is a solution for this equation because if p = -2,

p + 3 = -2 + 3

= 1

∴ Equation satisfied