Question

a : b = 1: 2, b : c = 3 : 2, d : c = 5 : 6, then find a : b : c : d.

Wrong answers will be reported.

Answer 1

Given

a : b = 1 : 2

=>
$\frac{a}{b} = \frac{1}{2} \\ \\ = > b = 2a \\ \\ = > a = \frac{b}{2}$

b : c = 3 : 2

=>
$\frac{b}{c} = \frac{3}{2} \\ \\ = > c = \frac{2b}{3}$

d : c = 5 : 6

=>
$\frac{d}{c} = \frac{5}{6} \\ \\ = > d = \frac{5c}{6} \\ \\ = > d = \frac{5}{6} \times \frac{2b}{3} \\ \\ (since \: c = \frac{2b}{3} ) \\ \\ = > d = \frac{5}{3} \times \frac{b}{3} \\ \\ = > d = \frac{5b}{9}$



So we got, a = b/2, c = 2b/3 and d = 5b/9

Hence, a : b : c : d

= b/2 : b : 2b/3 : 5b/9

cancel b

=> 1/2 : 1 : 2/3 : 5/9

Take LCM

=> 9/18 : 18/18 : 12/18 : 10/18

cancel 18

=> 9 : 18 : 12 : 10

Answer 2

a/b = 1/2

b/c = 3/2

let's multiply numerator and denominator by 2/3

b/c = 3× 2/3 )/ 2×2/3

= 2: 4/3

d:c =5:6

let's multiply numerator and denominator by 2/9

d:c = 5× 2/9 : 6× 2/9

= 10/9: 4/3

so a:b:c:d = 1:2: 4/3: 10/9

multiply it with 9

9:18: 12: 10 =a:b:c:d



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