Question

if four quantities ABCD be such that A : b = 3 : 4, B : C =5 : 6 ,c:d = 4:9 and then find continued ratio of ABCD

Answer 1

A:B = 3:4 , B:C = 5: 6 , C:D = 4:9

then A:B:C:D = ?

A/ B = 3/ 4 --(1) , B/ C = 5/ 6 --(2)

(A/ B) × (B/ C) = (3×5)/ (4 ×6)


A/ C = 15 / 24 = 5/ 8


thus A/ C = 5/ 8 , since C/ D = 4/ 9

then ,

(A/ C) × (C/ D) = (5×4)/ (8 ×9)


A/ D = 20/ 72 = 5/ 18

A/ D = 5/ 18 => A = 5D/ 18 ,

from(1) B = 4A/ 3 = 4( 5D/ 18) / 3


B = 20D/ 54 => B = 10D/ 27


from(2) C = 6B/ 5 = 6(10D/ 27) / 5


C = 60D/ 135 = 12D/27 = 4D/ 9


C = 4D/ 9

A:B:C:D =5D/18 :10D/27 : 4D/ 9 : D


=5/ 18 : 10/ 27 : 4/ 9 : 1


L.C.M ( 18, 27, 9,1 ) = 54


A:B:C:D = 5×3 : 10×2 : 4×6 : 54


A:B:C:D = 15 : 20: 24 : 54


Answer: A : B : C : D = 15 : 20 : 24 : 54