## 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 ?

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**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

T

T

*his 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

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**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

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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.

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**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 =

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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.

**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

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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 .

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**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

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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.

####
**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

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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 ).

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**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

Now dividing by 2 every terms, we have

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