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
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
, 4th and 5th numbers will be 1st , 2nd and 3rd numbers from column 2nd .
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
Now dividing by 2 every terms, we have
= 9 : 18 : 63 : 105 : 280 : 840
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