All of the three answer is 3,3,3

The same answer of all of them

Prime factors of 12 = {tex}2\times2\times3{/tex}

Prime factors of 81 ={tex}3\times3\times3\times3{/tex}

Prime factors of 48={tex}2\times2\times2\times2\times3{/tex}

Now, 3 is common in all the three numbers

So, 3 is the HCF

1. (a) Divisibility rule of 3: A number is divisible by 3 if sum of all the digits of the number is divisible by 3.

Here, _ + 6 + 7 + 2 + 4 = _ + 19

Therefore, the smallest digit is 2 so that the total will be 2 + 19 = 21, which is divisible by 3. So now, 26724 is divisible by 3.

Also, the greatest digit is 8 so that the total will be 8 + 19 = 27, which is divisible by 3, so now 86724 is divisible by 3.

    (b) Divisibility rule of 3: A number is divisible by 3 if sum of all the digits of the number is divisible by 3.

Here 4 + 7 + 6 + 5 + _ + 2 = _ + 24

Therefore, the smallest digit is 0 so that the total will be 0 + 24 = 24, which is divisible by 3. So now, 476502 is divisible by 3.

Also, the greatest digit is 9 so that the total will be 9 + 24 = 33, which is divisible by 3, so now 476592 is divisible by 3.

2. (a) Divisibility rule of 11: A number is divisible by 11 if the difference of the sums of digits of even places and that of odd places is either 0 or divisible by 11.

Here, Sum of even places = 8 + _ + 9 = 17 + _ and Sum fo odd places = 2 + 3 + 2 = 7

Therefore, the required digit is 1, so that the difference will be 18 - 7 = 11 and the number 921382 is divisible by 11

    (b) Divisibility rule of 11: A number is divisible by 11 if the difference of the sums of digits of even places and that of odd places is either 0 or divisible by 11.

Here, Sum of even places = 8 + 9 + 8 = 25 and Sum fo odd places = 4 + 4 + _ = 8 + _

Therefore, the required digit is 6, so that the difference will be 25 - 14= 11 and the number 869484 is divisible by 11.

Weight of medicine in each box = 4kg500g

= 4000+500 =4500g

Total weight the van can hold = 800kg 

=80,0000 g

Number of boxes = 80,0000/4500 =8000/45

= 177 boxes 

Ans. -32- 0.785 = -32.785

Proportion

An array is a systematic arrangement of similar objects , usually in rows and columns...

A set of data in which observations are arranged in ascending or desecending order is called an array.

Set of values is called as an array

{tex}(iii)3019:308{/tex}

(ii){tex}3325:308{/tex}

{tex}(i)3325:3019{/tex}

Money earned by Ravi = Rs. 13,300

Money saved by Ravi = Rs. 1224

Expenditure of Ravi = 13300-1224 = Rs.12076

1) Ratio of Salary : Saving

= 13300 : 1224

=3325 : 306

2) Salary : Expenditure

= 13300 :12076

=  3325:3019

3) Expenditure : saving

= 12076 :1224

=  3019:306

(i) 153:14

Money earned by Ravi = Rs. 15,300

Money saved by Ravi = Rs. 1400

Expenditure of Ravi = 15300-1400 = Rs.13900

1) Ratio of Salary : Saving

= 15300 : 400

=153 :4 

2) Salary : Expenditure

= 15300 :13900

= 153 :139

3) Expenditure : saving

= 13900 :1400

= 139 :14

I. By Division Method :

A) 0.360/120 = 0.003            B)  0.100/40 = 0.0025                                        C) 0.180/60 = 0.003

here we can find that A=B>C

II.  By Equalization Denominator :

A)  0.360/120                       B) 0.100/40 = 0.100X3 / 40X3 = 0.300/120            C) 0.180/60 = 0.180X2 / 60X2 = 0.360/120

here we find that when we do equal denominator then we see that A=B>C

perimeter of triangle= add all the length of sides

perimeter of equilateral triangle=3* length of a side

Ans. Perimeter of Equilateral Triangle = 3 * Side of triangle 

i will take example of this

we have to add 3.4+7.8

3 : 5 : : 6 : Z

5 x 6 = 3 x Z

30 = 3 x Z

Z = 30/3

Z = 10

the answer is 4

Diya gave 8 marbles and got back 7 .

So, now she has 7 marbles.

Out of this she gave 3 , she is left with 7-3= 4 marbles.

She got 10 marbles this time, so total number of marbles with her are 10 +4 = 14 marbles

Symmetry is a line which divides an object into 2 identical pieces which can overlap or superimpose each other

Perimeter of both chocolates will remain equal

Cadbury 1 has more perimeter .

Ans.

Centre

Ans. Mid-Point

Ans. We may observe that in 1 complete clockwise revolution, the hour hand will rotate by 360º.

From 2 to 8 it covers two right angles mean 180.

fraction : 180/360 = 1/2

Ans. 2 Kg is $\frac{5}{2}\%$ to 80 Kg and 25 Kg is 4 % to 625 Kg.

Let 2 Kg is y % of 80 Kg 

=> $\frac{80\times y}{100} = 2$

=> $y = \frac{2 \times 100}{80}$

=> $y = \frac{5}{2}\%$

Similarly, Let 25 Kg is z% of 625 Kg

Then, 

$\frac{625 \times z}{100} = 25$

=> $z = \frac{25 \times 100}{625}$

=> z = 4 %

In geometry, pyramids and prisms are two different shapes. The main difference between a pyramid and prism is the fact that a prism has two bases, while the pyramid only has one.

A pyramid is a three-dimensional polyhedron. The sides of the pyramid will always be triangular in shape. The sides of the pyramid meet the top. This is called the apex.

A prism is also a three-dimensional polyhedron. A prism has two identical ends and all flat sides. The sides or faces are perpendicular to the base faces, i.e. they make a right angle with the base.

A cube is a six sided 3 dimensional figure in which all the faces are square, a cuboid is the same except that some of the faces are rectangles. A cube is a 3-D version of a square and a cuboid is a 3-D version of a rectangle. All sides of a cube are of equal length but cuboid may have sides of different.

Trapezium : A 4-sided flat shape with straight sides that has a pair of opposite sides parallel. The sides that are parallel are called "bases". The other sides are "legs" (which may or may not be parallel)

Rhombus : A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. . All sides have equal length.

Parallelogram : A Parallelogram is a flat shape with opposite sides parallel and equal in length.

Let number of hens = x

Number of cows = y

Then number of legs of hens = 2x

Number of legs of cows = 4y

Then

According to Ques

x + y = 40 .......(1)

x = 40 - y

2x + 4y = 128 .....(2)

put value of x in (2)

2*(40-y) + 4y = 128

=> 80 - 2y + 4y =128

=> 2y = 48

y = 24

and x = 16

Electricity Bill : Telephone Bill :: 6 : 16

Let Bill paid for Electricity = 6k

& Bill paid for Telephone = 16k

As given, Telephone Bill - Electricity Bill = 800/-  => 16k - 6k = 800/-  => 10k = 800/- => k = 80/-

=> Electricity Bill = 6k = 6$\times$80/- = 480/-  & Telephone Bill = 16$\times$80/- = 1280/- (Answer)

Given Ratio  = 6 : 16

Let electrcity bill  = 6x

telephone bill = 16x

difference b/w both = 10x

it is given that this difference is 800.

so 10x = 800

x = 80

So electricity bill = 480

Telephone bill = 1280

Three quantities are said to be in continued proportion; if the ratio between the first and the second is equal to the ratio between the second and the third

Suppose, if we have three qualities such that the ratio of first to second is equal to the ratio of second to third, we say that the three qualities are in continued proportion. The middle term is called the mean proportional between the first the third terms.

i.e. a, b and c are in continued proportion, if a : b = b : c

The second quantity is called the mean proportional between the first and the third

i.e. in a : b = b : c; b is the mean proportional between a and c

 The third quantity is called the third proportional to the first and the second

i.e. in a : b = b : c; c is the third proportional to a and b

For example, let us consider the numbers 6, 12, 24.

Here the ratio of first quantity to the second = 6 : 12 = 1 : 2

And ratio of second quantity to the third = 12 : 24 = 1 : 2

We see that 6 : 12 = 12 : 24

Thus, 6, 12, 24 are in continued proportion.

The second quantity 12 is the mean proportional and third quantity 24 is the third proportional.

Solved example on continued proportion:

1. Find the mean proportion between 4 and 9.

Solution:

Let the mean proportion be x

Therefore, 4 : x = x : 9

⇒ x × x = 4 × 9

⇒ x^2 = 36

⇒ x^2 = 6^2

⇒ x = 6

2. Find, m, if 7, 14, m are in continued proportion.

Solution:

x, y and z are in continued proportion xz = y^2

Let 7, 14, and m be x, y and z respectively.

Therefore, 7m = 14^2

or, 7m = 196         

or, m = 196/7

Therefore, m = 28.

Hence, m = 28.

3. Find the third proportional to 12 and 30.

Solution:

Let x be the third proportional

Therefore, 12 : 30 = x : 30

⇒ 12 × x = 30 × 30

⇒ 12x = 900

⇒ x = 900/12

⇒ x = 75

Basically to find the Loss you need to subtract the CP to the SP 

The equation is = C P - SP

In numbers it will be 40 - 20 = 20

Loss = CP - SP

in given Question CP = 40 

SP = 20

So Loss = 40 - 20 = 20

Loss is when you sell the thing less than its Cost Price(CP) so that Selling Price(SP) SP<CP

So Loss=CP-SP

Loss=40-20=20

A parabola is U shaped curve which is function of quadric equation y=x2 . The parabola is locus of points in the plane that are equidistant from both the directrix and the axis. 

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and a fixed straight line (the directrix )

We will apply the BODMAS Rule 

BODMAS= Bracket off ,division, multiplication, addition and subtraction

25÷5 +12- 2 

The first operation is division .so we divide 25÷5 =5 

5 +12-2 

The second part is addition 

5+12=17 

17-2=15