If 4a=5b and 8b=9c find a:b:c.?

Method 1 :

4a = 5b
a = 5b/4

8b = 9c
c = 8b/9

a : b : c
= (5b/4) : b : (8b/9)
= (5/4)*36 : 1*36 : (8/9)*36
= 45 : 36 : 32


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Method 2 :

4a = 5b
a/b = 5/4
a : b = 5 : 4
Hence, a : b = 45 : 36 …… [1]

8b = 9c
b/c = 9/8
b : c = 9 : 8
Hence, b : c = 36 : 32 …… [2]

Refer to [1] and [2] :
a : b : c = 45 : 36 : 32

4a = 5b
b = (4/5)a

8b = 9c
c = (8/9)b
 = (8/9)(4/5)a
 = (32/45)a

a:b:c = 1:(4/5):(32/45)
   = 45:36:32