Question

a:b=1:2; b:c=3:4; c:d= 6:9;d:e = 12:16 find the value of a:b:c:d:e​

Answer 1

Given:-

• A : B = 1:2
• B : C = 3 : 4
• C : D = 6: 9
• D : E = 12 : 16

To find :-

• A : B : C : D : E

SOLUTION :-

A : B = 1: 2

B : C = 3:4

In this B is the common Since LCM of B ratio 2, 3 is 6

In order to get ratio of B same as 6 So, multiply with 3

A : B = 1:2 (3)

A : B = 3:6

B : C = 3:4 (2)

In order to get ratio of B same as 6 So, multiply with 2

B : C = 6 : 8

A : B : C = 3:6 : 8

Multiply A : B : C with 3 In order to find the ratio of A : B : C :D

A : B : C = (3:6:8)3

A: B : C = 9: 18 : 24-------EQ 1

Now, if you observe ratio of B is same

Since , B : C = 6: 8

Now , C : D = 6: 9

C ratio is not same LCM of 8, 6 is 24

B : C = (6:8)3

B : C = 18 : 24

C : D = (6: 9) 4

C : D = 24 : 36

A : B : C : D = 9 : 18: 24 : 36 ----- EQ 2

C : D = 24 :36

D : E = 12 : 16

Here D ratio is same Hence LCM of 36 , 12 is 36

C : D = (24:36) 1

C : D = 24 : 36

D : E = (12:16) 3

D : E = 36 : 48

Now D ratio is same

C : D :E = 24 : 36 : 48 ------ EQ 3

If you observe equation 2, 3 ratio of C , D are same

A : B : C : D : C : D :E = 9 :18 :24 : 36 : 24 : 36 : 48

A : B : C : D : E = 9: 18 : 24 : 36 : 48

Simplifying this

A : B : C : D : E = 3 : 6 : 8 : 12 : 16

So, the ratio of A : B : C : D : E = 3 : 6 : 8 : 12 : 16