Algebra

(a)

From the above figure, it can be observed that the letter T will require 2 matchsticks

Therefore,

The pattern is 2n

(b)

From the above figure, it can be observed that the letter Z will require 3 matchsticks

Therefore,

The pattern is 3n

(c)

From the above figure, it can be observed that the letter U will require 3 matchsticks

Therefore,

The pattern is 3n

(d)

From the above figure, it can be observed that the letter V will require 2 matchsticks

Therefore,

The pattern is 2n

(e)

From the above figure, it can be observed that the letter E will require 5 matchsticks

Therefore,

The pattern is 5n

(f)

From the above figure, it can be observed that the letter S will require 5 matchsticks

Therefore,

The pattern is 5n

(g)

From the above figure, it can be observed that the letter R will require 6 matchsticks

Therefore,

The pattern is 6n

We know that, the letter L requires 2 matchsticks

Therefore,

The pattern for L will be 2n

Now, if we look the letters given in the question 1 then there are only T and V which require only only two matchsticks

Hence, T and V have same pattern as that of L.

Let us assume the number of rows will be n.

Also,

It is given in the question that:

Number of cadets in one row = 5

Therefore,

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

= n × 5

= 5n

Let us assume the number of boxes be "b".

Also, it is given in the question that:

Number of mangoes in a box = 50

Therefore,

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

= b × 50

= 50b

Let us assume the number of students be s

Also,

It is given in the question that:

Number of pencil given to each student = 5

Therefore,

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

= 5 × s

= 5s

Let us assume the flying time be "t" minutes

Also,

Distance covered in 1 min = 1 km

Therefore, the distance covered in t minutes = Distance covered in one minute × Flying time

= 1 × t

= t km

It is given in the question that,

Number of dots in 1 row = 9

Also,

Number of rows = r

Therefore,

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

= 9 × r

= 9r

Hence,

Number of dots in 8 rows = 8 × 9 = 72

Also,

Number of dots in 10 rows = 10 × 9 = 90

Let us assume the age of Radha be x years

It is given in the question that,

Age of Leela = Age of Radha – 4

Therefore,

Leela’s Age = (x – 4) years

It is given that,

Number of laddus given away = l

Also,

Number of laddus remaining = 5

Therefore,

Total number of laddus = Number fo laddus given away + Number of laddus remaining

= l + 5

Hence,

Total number of laddus be l + 5

Given in the question that,

Number of oranges in one small box = x

Therefore,

Number of oranges in two small boxex = 2x

Also,

Total number fo oranges left = 10

Hence,

Number of oranges in the large box = Number of oranges in two small boxes + Number fo oranges left

= 2x + 10

Therefore,

There will be 2x + 10 oranges in the large box.

From the above-given figures, it can be observed that,

The number of matchsticks in the above-given pattern are 4, 7, 10 and 13 respectively.

4 = 3(1) + 1

7 = 3(2) + 1

10 = 3(3) + 1

i.e., The matchstick is 1 more than the thrice of the number of squares in the pattern

Hence,

The pattern for above-given figures will be:

3n + 1

Where n is the number of squares

From the above given figures it can be observed that,

The number of matchsticks in the above given pattern are 3, 5, 7 and 9 respectively

i.e., The matchstick are 1 more than the twice of the number of triangles in the pattern

Hence,

The pattern for above given figures will be:

2n + 1

Where n is the number of triangles

It is given in the question that,

Side of equilateral triangle = l

We know that,

The perimeter of equilateral triangle = Sum of all sides of the triangle

Therefore,

Perimeter of the equilateral triangle = l + l + l

= 3l

It is given in the question that,

Side of regular hexagon = l

We know that,

Perimeter of regular hexagon = 6 × side

Therefore,

Perimeter of regular hexagon = 6 × l

= 6l

It is given in the question that,

Length of edge of cube = l

Also,

Number of edges in the cube = 12

Therefore,

Total number of edges = Number of edges × Length of the edge

= 12 × l

= 12l

Here,

In the given question,

We know that,

CP is the radius r of the circle

And,

AB is the diameter of the circle,

And,

C is the centre of the circle

We can also see that,

AB = 2CP

Hence,

We can say that,

The diameter of the circle is two times the radius of the circle.

Here,

Let us take any three numbers as a, b and c.

Now,

According to the question,

We have to express the associative property here

And,

We know that,

Associative property says that,

Among three numbers any two numbers added together and then the resultant added to the third one will give the same result.

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

In this question,

Most of the expressions can be formed by using the numbers 5, 7 and 8

Some of the examples of these expressions are as follows:

5 × (8 – 7)

5 × (8 + 7)

(8 + 5) × 7

(8 – 5) × 7

(7 + 5) × 8

(7 – 5) × 8

from the given parts it is clear that:

(a), (b), (e), (f) and (g) are the expressions which have both letters and numbers

Whereas,

(c) and (d) are those expression which are formed by using numbers only

(a) From the above given expression it is clear that:

Firstly,

Addition, as 1 is added to z

Then,

Subtraction, as 1 is subtracted from z

Then,

Addition, as 17 is added to y

At last,

Subtraction, as 17 is subtracted from y

(b) From the above-given expression, it is clear that:

Firstly,

Multiplication, as y is multiplied with 17

Then,

Division, as y is divided by 17

Then,

Multiplication as z is multiplied with 5

(c) From the above-given expression, it is clear that:

Firstly,

There is multiplication and addition as:

y is multiplied with 2 and 17 is added to the result

Then,

There are multiplication and subtraction as:

y is multiplied with 2 and 17 is subtracted from the result

(d) From the above-given expression, it is clear that:

Firstly,

Multiplication, as m is multiplied with 7

Then,

There are multiplication and addition as m is multiplied with -7 and 3 is added to the result

At last,

There are multiplication and subtraction as:

m is multiplied with -7 and 3 is subtracted from the result

(a) The expression for the above given case is as follows:

p + 7

(b) The expression for the above given case is as follows:

p - 7

(c) The expression for the above given case is as follows:

7 × p = 7p

(d) The expression for the above given case is as follows:

(e) The expression for the above given case is as follows:

- m - 7

(f) The expression for the above given case is as follows:

- 5p

(g) The expression for the above given case is as follows:

-

(h) The expression for the above given case is as follows:

- 5p

(a) The expression for the above given case is as follows:

2m + 11

(b) The expression for the above given case is as follows:

2m – 11

(c) The expression for the above given case is as follows:

5y + 3

(d) The expression for the above given case is as follows:

5y – 3

(e) The expression for the above given case is as follows:

- 8y

(f) The expression for the above given case is as follows:

- 8y + 5

(g) The expression for the above given case is as follows:

16 – 5y

(h) The expression for the above given case is as follows:

- 5y + 16

The expressions for the above given case by using t and 4 is as follows:

t + 4

t – 4

4t

4 – t

4 + t

The expressions for the above-given case by using y, 2 and 7 is as follows:

2y + 7, 2y – 7, 7y + 2,…..

The answers of the parts are answered below:

(i) We know that,

Sarita’s present age is y

Hence,

Sarita’sage five years from now will be = Sarita’s present age + 5

= y + 5

(ii) We know that,

Sarita’s present age is y

Hence,

Sarita’s age three years ago will be = Sarita’s present age – 3

= y – 3

(iii) We know that,

Sarita’s present age is y

Hence,

Sarita’s grandfather’s age will be = Sarita’s present age × 6

= 6y

(iv) We know that,

Grandfather’s age is 6y

Hence,

Grandmother’s age will be = Grandfather’s age – 2

= 6y – 2

(v) We know that,

Sarita’s present age is y

Hence,

Sarita’s father’s age = 5 + 3 × Sarita’s present age

= 5 + (3 × y)

= 5 + 3y

According to the question,

We know that,

The breadth of the rectangular hall is b metres

Therefore,

Length of the rectangular hall = 3 × breadth – 4

l = (3 × b) – 4

l = 3b – 4

Hence,

The length will be (3b – 4) metres.

Here,

It is given in the question that,

The height of the rectangular box = h

Now,

We have to express the length and breadth in terms of height

Thus,

Let the length of the rectangular box be l

And,

The breadth of the rectangular box be b

Hence,

Length of the box = 5 × height

l = 5h cm

Breadth of the box = 5 × height – 10

b = (5h – 10) cm

Here,

According to the question,

We know that,

Meena is at step s

Now,

Step at which Beena is = (Step at which Meena is) + 8

= s + 8

And,

Step at which Leena is = (Step at which Meena is) – 7

= s – 7

Hence,

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

= 4 × s – 10

= 4s – 10

Here,

According to the question,

We know that,

Speed = v km/hr

Now,

We have to calculate the distance between Daspur to Beespur

So,

At first we need the distance travelled in 5 hours

Thus,

Distance traveled in five hours = 5 × v

= 5v

Hence,

The total distance between Daspur and Beespur = (dist. Travelled in 5 hours) + 20

= 5v + 20

(a) Here,

In the given question,

We know that,

Cost of a notebook = Rs p

And,

Cost of book = Rs 3p

Hence,

We can clearly observe that,

A book costs three times the cost of a notebook.

(b) Here,

In the given question,

We know that,

Number of marbles Tony puts on the table = q

And,

Number of marbles Tony has in his box = 8q

Hence,

We can clearly observe that,

Tony’s box contains 8times the number of marbles on the table.

(c) Here,

In the given question,

We know that,

Number of students in our class = n

And,

Total number of students in the school = 20n

Hence,

We can clearly observe that,

The total number of students in the school is 20 times the student in our class.

(d) Here,

In the given question,

We know that,

Age of Jaggu = z years

And,

Age of his uncle = 4z

And,

Age of his aunt = 4z - 3

Hence,

We can clearly observe that,

Jaggu’s uncle is 4 times older than Jaggu.

And,

Jaggu’s aunt is 3 years younger than his uncle.

(e) Here,

In the given question,

We know that,

Number of rows = r

And,

Number of dots in each row = 5

Hence,

We can clearly observe that,

The total number of dots is 5 times the number of rows.

Here,

According to the question,

We can conclude that,

(x – 2) represents that the person, whose age is (x – 2) years, is two years younger to Munnu.

And,

(x + 4) represents that the person, whose age is (x + 4) years, is four years elder to Munnu.

And,

(3x + 7) represents that the person, whose age is (3x + 7) years,

is elder to Munnu and his age is 7 years more than thrice the age of Munnu.

At first,

In future,

Sara’s age will be (y + n), after n years from now.

Now,

In past,

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

Now,

According to the question,

We can conclude that,

(y + 7) represents that the person, whose age is (y + 7) years, is 7 years elder to Sara.

And,

(y -3) represents that the person, whose age is (y – 3) years, is 3 years younger than Sara.

And,

(y + ) represents that the person, whose age is (y + ) years, is years elder to Sara.

And,

(y -) represents that the person, whose age is (y – ) years, is years younger than Sara.

Here,

According to the question,

We can conclude that,

2n may represent the number of person who either likes football or some other game such as cricket

Whereas,

represents the number of students who like cricket, out of the total number of students who like either football or cricket.

(a) 17 = x + 7


From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(b) (t-7) > 5

It does not have "=" sign.

It is not an equation.

(c) = 2

From the above given equation we can see that it has "=" sign without a variable.

Hence it is not an equation with variable.

(d) 7 × 3 – 19 = 8

From the above given equation we can see that it has "=" sign without a variable.

Hence it is not an equation with variable.

(e) 5 × 4 – 8 = 2x

From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(f) x – 2 = 0

From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(g) 2m< 30

It does not have "=" sign.

It is not an equation.

(h) 2n + 1 = 11

From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(i) 7 = (11×5) – (12×4)

From the above given equation we can see that it has "=" sign without a variable.

Hence it is not an equation with variable.

(j) 7 = (11×2) + p

From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(k) 20 = 5y

From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(l) < 5

It does not have "=" sign.

It is not an equation.

(m) z + 12 > 24

It does not have "=" sign.

It is not an equation.

(n) 20 – (10-5) = 3×5

From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(o) 7 – x = 5

From the above given equation we can see that it has "=" sign with a variable.

Hence it is an equation.

(a) 10 y = 80
We have,

10 y = 80

Now,

y = 10 is not a solution for the above given equation because:

When, y = 10

10 y = 10 × 10

= 100

And,

100 80

(b) 10 y = 80
We have,

10 y = 80

Now,

y = 8 is a solution for the above given equation because:

When, y = 8

10 y = 10 × 8

= 80

And,

80 80

(c) 10 y = 80
We have,

10 y = 80

Now,

y = 5 is not a solution for the above given equation because:

When, y = 5

10 y = 10 × 5

= 50

And,

50 80

(d) 4 l = 20
We have,

4 l = 20

Now,

l = 20 is not a solution for the above given equation because:

When, l = 20

4 l = 4 × 20

= 80

And,

80 20

(e) 4 l = 20
We have,

4 l = 20

Now,

l = 80 is not a solution for the above given equation because:

When, l = 80

4 l = 4 × 80

= 320

And,

320 20

(f) 4 l = 20
We have,

4 l = 20

Now,

l = 5 is a solution for the above given equation because:

When, l = 5

4 l = 4 × 5

= 20

And,

20 20

(g) b + 5 = 9
We have,

b + 5 = 9

Now,

b = 5 is not a solution for the above given equation because:

When, b = 5

b + 5 = 5 + 5

= 10

And,

10 9

(h) b + 5 = 9
We have,

b + 5 = 9

Now,

b = 9 is not a solution for the above given equation because:

When, b = 9

b + 5 = 9 + 5

= 14

And,

14 9

(i) b + 5 = 9
We have,

b + 5 = 9

Now,

b = 4 is a solution for the above given equation because:

When, b = 4

b + 5 = 5 + 4

= 9

And,

9 = 9

(j)h - 8 = 5
We have,

h - 8 = 5

Now,

h = 13 is a solution for the above given equation because:

When, h = 13

h - 8 = 13 - 8

= 5

And,

5 5

(k) h - 8 = 5
We have,

h - 8 = 5

Now,

h = 8 is not a solution for the above given equation because:

When, h = 8

h - 8 = 8 - 8

= 0

And,

0 5

(l)h - 8 = 5
We have,

h - 8 = 5

Now,

h = 0 is not a solution for the above given equation because:

When, h = 0

h - 8 = 0 - 8

= -8

And,

-8 5

(m) p + 3 = 1
We have,

p + 3 = 1

Now,

p = 3 is not a solution for the above given equation because:

When, p = 3

p + 3 = 3 + 3

= 6

And,

6 1

(n)p + 3 = 1
We have,

p + 3 = 1

Now,

p = 1 is not a solution for the above given equation because:

When, p = 1

p + 3 = 1 + 3

= 4

And,

4 1

(o) We have,

p + 3 = 1

Now,

p = 0 is not a solution for the above given equation because:

When, p = 0

p + 3 = 0 + 3

= 3

And,

3 1

(p) p + 3 = 1
We have,

p + 3 = 1

Now,

p = -1 is not a solution for the above given equation because:

When, p = -1

p + 3 = - 1 + 3

= 2

And,

2 1

(q) p + 3 = 1
We have,

p + 3 = 1

Now,

p = -2 is a solution for the above given equation because:

When, p = -2

p + 3 = - 2 + 3

= 1

And,

1 = 1

Therefore,

The equation is satisfied

(a)5m = 60 (10, 5, 12, 15)

Hence m = 12 is the solution.
We have,

5m = 60

m = 12 is the solution for given equation as,

When m = 12

5m = 5 × 12

= 60

Hence, the equation is satisfied

m = 10 is not a solution to the given equation because:

When m = 5

5m = 5 × 5

= 25

And, 25 60

Also,

m = 15 is not a solution to the given equation because:

When m = 15

5m = 5 × 15

= 75

And, 75 60

(b) We have,

n + 12 = 20

n = 8 is the solution for given equation as,

When n = 8

n + 12 = 8 + 12

= 20

Hence, the equation is satisfied

n = 12 is not a solution to the given equation because:

When n = 12

n + 12 = 12 + 12

= 24

And, 24 20

Also,

n = 20 is not a solution to the given equation because:

When n = 20

n + 12 = 20 + 12

= 32

And, 32 20

n = 0 is not a solution to the given equation because:

When n = 0

n + 12 = 0 + 12

= 12

And, 12 20

(c) We have,

p - 5 = 5

p = 10 is the solution for given equation as,

When p = 10

p - 5 = 10 - 5

= 5

Hence, the equation is satisfied

p = 0 is not a solution to the given equation because:

When p = 0

p - 5 = 0 - 5

= - 5

And, -5 5

Also,

p = 5 is not a solution to the given equation because:

When p = 5

p - 5 = 5 - 5

= 0

And, 0 5

p = -5 is not a solution to the given equation because:

When p = -5

p - 5 = -5 - 5

= - 10

And, - 10 5

(d) We have,

= 7

q = 14 is the solution for given equation as,

When q = 14

=

= 7

Hence, the equation is satisfied

q = 7 is not a solution to the given equation because:

When q = 7

=

And, 7

Also,

q = 2 is not a solution to the given equation because:

When q = 2

=

= 1

And, 1 7

q = 10 is not a solution to the given equation because:

When q = q0

=

= 5

And, 5 7

(e) We have,

r - 4 = 0

r = 4 is the solution for given equation as,

When r = 4

r - 4 = 4 - 4

= 0

Hence, the equation is satisfied

r = - 4 is not a solution to the given equation because:

When r = - 4

r - 4 = - 4 - 4

= - 8

And, - 8 0

Also,

r = 8 is not a solution to the given equation because:

When r = 8

r - 4 = 8 - 4

= 4

And, 4 0

r = 0 is not a solution to the given equation because:

When r = 0

r - 4 = 0 - 4

= - 4

And, - 4 0

(f) We have,

x + 4 = 2

x = - 2 is the solution for given equation as,

When x = - 2

x + 4 = - 2 + 4

= 2

Hence, the equation is satisfied

x = 0 is not a solution to the given equation because:

When x = 0

x + 4 = 0 + 4

= 4

And, 4 2

Also,

x = 2 is not a solution to the given equation because:

When x = 2

x + 4 = 2 + 4

= 6

And, 6 2

x = 4 is not a solution to the given equation because:

When x = 4

x + 4 = 4 + 4

= 8

And, 8 2

For m + 10, the table can be formed as follows:

From the above solution, we find that:

m = 6 is the solution of the given equation as

m + 10 = 6 + 10

= 16

For 5t, the table can be formed as follows:

From the above solution, we find that:

t = 7 is the solution of the given equation as

5t = 5 × 7

= 35

For the table can be formed as follows:

From the above solution, we find that:

z = 12 is the solution of the given equation as

For z = 12,

= 4

The table can be formed as follows:

From the above solution, now we have to find the solution for: m - 7 = 3

This is the solution when m = 10 (in the table)

Thus, m = 10 is the solution of the given equation.

(i) From above riddle, we can conclude following:

We know that,

There are 4 corners in a square

Also,

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

When 12 is added to the number than we get the result which is 34

Hence,

The number must be the difference of 34 and 12

i.e., 34 – 12 = 22

(ii) From above riddle, we can conclude following:

When the old number was up counted on Sunday then the result was 23

Also,

When the old number was up counted on Saturday then the result was 22

When the old number was up counted on Friday then the result was 21

When the old number was up counted on Thursday then the result was 20

When the old number was up counted on Wednesday then the result was 19

When the old number was up counted on Tuesday then the result was 18

When the old number was up counted on Monday then the result was 17

Therefore,

Number taken at start = 17 – 1

= 16

(iii) From above riddle, we can conclude following:

We know that,

Total players in a cricket team = 11

Therefore, according to the riddle the number is such that when 6 is subtracted from it the result is 11

Hence,

Required number = 11 + 6

= 17

(iv) From above riddle, we can conclude following:

According to the riddle the number is such that when it is subtracted from 22 then the result will be the number itself

Therefore,

The required number should be 11 which again gives 11 when it is subtracted from 22