Question

if a:b3:4b:c=5:6and c:d=11:9 then a:d is

Answer 1

Given,
a:b = 3:4
=> a/b = 3/4 --------------------------->(1)

b:c = 5:6
=> b/c = 5/6 -------------------------->(2)
(1) × (2) => a/b × b/c = 3/4 × 5/6
=> a/c = 5/8 ------------------>(3)
Again,
c:d = 11:9
=> c/d = 11/9 ----------------------------------->(4)

(3) × (4) => a/c × c/d = 5/8×11/9
=> a/d = 55/72

Therefore, a:d = 55:72 .

Answer 2

a : b = 3 : 4 = 3 x 5 : 4 x 5 = 15 : 20

b : c = 5 : 6 = 5 x 4 : 6 x 4 = 20 : 24

( Multiplied for equalizing b in both, here it would have been 20.)

∴ a : b : c = 15 : 20 : 24

∴ a : c = 15 : 24 = 5 x 3 : 8 x 3 = 5 : 8

a : c = 5 : 8 = 5 x 11 : 8 x 11 = 55 : 88

c : d = 11 : 9 = 11 x 8 : 9 x 8 = 88 : 72

( Multiplied for equalizing c in both, here it would have been 88.)

∴ a : c : d = 55 : 88 : 72

∴ a : d = 55 : 72