How to find proportion of Four numbers

How to find proportion of 4 numbers, proportion of Four numbers with the help of examples

What is Proportion

Proportion is majorly based on ratio and fractions. A fraction is written in the form of a/b, while ratio a:b, then a proportion means that two ratios are equal. Here a and b are any two numbers. The ratio and proportion are key foundations to understand the various concepts in mathematics .

Proportion can be applied to solve many daily life problems based on mixture ,work and time , time and speed etc . It develops a relation between two or more quantities and thus helps in their comparison.

What is Proportion?

Proportion in general is referred to as a part, share, or number considered in comparative relation to a whole. Proportion says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal .

How to find proportion of Four numbers

If A : B = 2 : 3, B : C = 4 : 5 and      C : D = 6 : 7,    what is A  : D  ?

How to find A : B : C : D

Let  us mark these columns 1st and 2nd  as follows 

                      1   2

A   :    B =     2    :   3 

B    :     C =    4    :   5

C     :     D =    6    : 7

The value of A can be calculated by taking product  of all numbers  appearing under column (1).Therefore  A is product of  2 , 4 and 6

A = 2 x 4 x 6 = 48

The value of B can be calculated by  product under column (1) beginning from second row and numbers  under column (2) for all previous rows. Therefore  B is product of  4 , 6 and 3

B = 4 x 6 x 3 = 72

Similarly C can be computed  by taking  product of all numbers  under column (1) beginning from third row and terms under column (2) for all previous rows.Hence  C is product of  6 ,3 and 5

C = 6 x 3 x 5 = 90

D is result  of all terms appearing under column (2).

D = 3 x 5 x 7 = 105

=> A:B:C:D = 48 : 72 : 90 : 105

Ratio between any two or three variables from above.

A  : D = 48  :   105 = 16  :  35
This logic can be applied  to any number of rows

If A:B,  B:C,  C:D, D:E and E:F are  given, we can find A : B : C : D : E : F using above method.

Example :

A:B = 1:2

B:C = 2:7

C:D = 3:5

D:E = 3:8

E:F = 1:3

To find value of  A

To find out value of A multiply all the numbers which are under 1st column starting from this Row . We must choose one number less  to multiply as the variables ( A, B, C ,D and E ).

A = 1 × 2 × 3 × 3 ×1 = 18

To find value of  B

To find out value of B multiply all the numbers which are under 1st column starting from this Row  ( here four numbers are in 1st column which are below  A ,so our 5th number will be 1st number from column 2nd.

B = 2 × 3 × 3 × 1 × 2 = 36

To find value of  C

To find out value of C multiply  all the numbers which are under 1st column starting from this Row ( here three numbers are in 1st column which are below  B ,so our 4th and 5th numbers  will be 1st and 2nd numbers  from column 2nd.

C =  3 × 3 × 1 × 2 × 7 =126

To find value of  D

To find out value of C multiply  all the numbers which are under 1st column starting from this Row ( here two numbers are in 1st column which are below  C , so our 3rd
,  4th  and 5th numbers will be 1st , 2nd and 3rd numbers  from column 2nd .

D = 3 × 1 × 2 × 7 × 5 = 210

To find value of  E

To find out value of C multiply  all the numbers which are under 1st column starting from this Row ( here 1st  numbers is in 1st column which are below  D ,so our 2nd ,3rd , 4th and 5th number will be 1st ,2nd ,3rd and 4th number from column 2nd.

E = 1 × 2 × 7 × 5 × 8 = 560

To find value of  F

To find out value of F multiply all the numbers which are under 2nd column starting in front of  1st Row . We must choose one number less  to multiply as the variables ( A, B, C ,D and E ).

F = 2 × 7 × 5 × 8 × 3 = 1680

     A  :   B   :   C   :      D  :     E   :  F

= 18  :  36  : 126 : 210   : 560   : 1680
Now dividing  by 2 every terms,  we have 

= 9   : 18  : 63  : 105   :  280   :  840

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Most Important Reasoning questions with answers for competitive exams

Most Important Reasoning questions with answers for competitive exams of number analogy with solutions have been discussed in this post . These types of problems are very helpful for cracking competitive exams like ssc cgl, ssc chsl and various Bank exams and many other similar exams. please feel free to comment your opinions. 

What is next terms in the series ?

Let us solve next number in sequence puzzle

15, 29, 56, 108, 208, ????

Here 1st term is 15, To find out 2nd term if we multiply the 1st term With 2 and subtract 1 from it, i.e (15 × 2) -1  = 30 - 1= 29

To find 2nd term we have to multiply the previous term with 2 and subtract 2 (double the previous time) from it

i.e (29 × 2) - 2 = 58 - 2 = 56

To find 3rd term we have to multiply the previous term with 4   and subtract 2  (double the previous time) from it

i.e  (56 × 2) - 4 = 112 - 4 = 108

To find 4th term we have to multiply the previous term with 8 (double the previous time) and subtract 2 from it

i.e (108 × 2) - 8 = 216 - 8 =  208

Similarly 5th term can be calculated as

multiply the previous term with 2 and subtract  subtract 2 (double the previous time) from it

i. e.  (208 × 2) - 16 = 416 - 16 =  400

Next term (400×2) - 32 = 800 - 32 =  768

Next term  (768 × 2) - 64 = 1536  - 64 = 1472

Next term  (1472 × 2) - 128 = 2944 - 128  =2816

Or we can write it in another form as follows

15 + (15–1) = 15 + 14= 29

29 + (29–2) = 29 + 27 = 56

56 + (56–4) = 56 + 52 = 108

108 + (108–8) =108 + 100 = 208

208 + (208–16) = 208 + 192= 400

400 + (400–32) = 400 + 368 = 768

768 + (768–64) = 768 + 704 = 1472

1472 + (1472-128) = 1472 + 1344 = 2816

And similarly this trend follows

What’s the next number in the sequence 0, 2, 6, 12 , ?

We can get the answer in two  ways

1st Method

1 × (1–1) = 0 ( 1st term)

2 × (2–1) = 2 (2nd term)

3 × (3–1) = 6 (3rd term)

4 × (4–1) = 12 (4th term)

5 × (5–1) = 20 (5th term) 

Next term must be  20
Similarly 
6 × (6–1) = 30  (6th term)

7 × (7–1) = 42  (7th term)

2nd Method

1² – 1 = 1 - 1  = 0

2² –  2 = 4 - 2 = 2 

3² – 3 = 9 - 3 = 6

4² – 4 = 16 - 4 = 12 

5² – 5 = 25 - 5 =  20 
Next term must be  20
Similarly 

6² – 6 = 36 - 6 = 30 

7² – 7 = 49 - 7=  42

Can you solve this  Series: 30, 31, 28, 33, 26, 35, … What number should come next?

We can split this sequence into two series by picking alternate numbers from the given sequence. 
30, 31, 28, 33, 26, 35, …
1st  one is 30,  28, 26, … and 2nd one is  31, 33,  35, …
Now after careful analysing the 1st sequence ,its next terms should be  with decrease of  2 ,we get other terms as follows 
30,  28, 26, 24, 22 ,20 …
And after careful analysing the 2nd  sequence ,its next terms should be  with increase of  2 ,we get other terms as follows 
31, 33,  35, 37, 39 ,41… 

26 - 2 = 24.
So the text terms should be 30, 31, 28, 33, 26, 35, 24, 37, 22 

24 is the next number in the required sequence.

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HOW TO ADD 1 TO 1000 NUMBERS VERY EASILY

HOW TO ADD 1 TO 1000 NUMBERS VERY EASILY

If you want to add 1 to 1000 then follow these two steps

1  Add 1 to last number 

2 Multiply last number and it's next numbers then divide by 2 . And thats it  .

अगर आप 1 से लेकर किसी भी अंतिम संख्या को जोड़ना चाहते हो तो सबसे पहले अंतिम संख्या में एक जोड़ दें फिर अंतिम संख्या और उससे आगे बाली संख्या को गुणा करके 2 से भाग दे दें ,आप इस तरह से कितनी भी शंख्ययाओं का जोड़ एक दम से कर सकते हो

उदाहरण

If we have to add 1st 50 numbers then  Multiply 50 with 51 and divide the product with 2 and it is the sum of 1st 50 natural numbers 

 अगर हम 1 से 50 को जोड़ना चाहें तो 50 और 51 गुना करके 2 से भाग देंगे

1 +2+3+4+5+6+7+……+50 =(50×51)÷2 = 25×51=1275

अगर हम 1 से 100 को जोड़ना चाहें तो 100 और 101 गुना करके 2 से भाग देंगे

1+2+3+4+5+…….+100=( 100×101) ÷2 =50×101=5050

अगर हम 1 से 1000 को जोड़ना चाहें तो 1000 और 1001 गुना करके 2 से भाग देंगे

1+2+3+4+5+…….+1000 =(1000×1001)÷2 = 500×1001= 500500

अगर हम 1 से 2000 को जोड़ना चाहें तो 2000 और 2001 गुना करके 2 से भाग देंगे

1+2+3+4+5+…….+2000=( 2000×2001)÷2 =1000×2001 = 2001000

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How to find shortest distance between two lines

SHORTEST DISTANCE BETWEEN TWO LINES

1st of all we shall find out shortest distance between two Parallel lines.

Problem 1

Consider two parallel lines whose equations in vector form are given by

 Now comparing these equations with standard form , and write

 _, and  vectors ,we get

Now applying this formula to find the shortest distance between two lines .

As it is clear from formula , we have to find cross product of  and  and then magnitude of vector 

Now find the magnitude of  × vector

                                 =√(81)+(196)+(16)

                                 =√293

Magnitude of 

                    = √49

           = 7

Putting all these values in  the formula of Shortest Distance between two lines .

Now Find distance between two skew lines i.e. Lines which are not Parallel lines.

Problem 2

Consider two parallel lines whose equations in vector form are given by

 Now comparing these equations with standard form , and write

 _, and  vectors ,we get

 Now applying this formula to find the shortest distance between two lines 

 Now find cross product and then  magnitude of these two vectors

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Thanks for watching and responding to this post "HOW TO FIND SHORTEST DISTANCE BETWEEN TWO LINES".

My previous Posts

HOW TO SOLVE LINEAR EQUATIONS OF THREE  VARIABLES  BY  MATRIX  METHOD

 How to find area bounded by two circles 

 How to integrate integral with square root in numerator     

How to find area of the circles which is interior to the parabola
How to find common area of two parabolas.

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If you are a mathematician Don't forget to visit my Mathematics You tube channel , Mathematics Website and Mathematics Facebook Page , whose links are given below

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