## 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 ?

We shall find A : B : C : D

**How to find A : B : C : D**

Let us mark these columns as follows

**1 2**

A : B = 2 : 3

B : C = 4 : 5

C : D = 6 : 7

*The value of A can be calclulated 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 calclulated 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 find out 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

A = 1 × 2 × 3 × 3 ×1 = 18

B =

**2 × 3**× 3 × 1 × 2 = 36
C = 3 × 3 × 1 × 2 × 7 =126

D = 3 × 1 × 2 × 7 × 5 = 210

E = 1 × 2 × 7 × 5 × 8 = 560

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