- (A) 1 : 5 :6
- (B) 1 : 3 : 2
- (C) 3 : 2 :1
- (D) 2 : 1 : 6
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If A : B = 2 : 1 and A : C = 1 : 3, then A : B : C is:
If A : B = 2 : 1 and A : C = 1 : 3, then A : B : C is:
Correct option is (D) 2 : 1 : 6
Solution:
To find (A : B : C) given (A : B = 2 : 1) and (A : C = 1 : 3)
Firstly, express (A) in terms of (B) and (C):
From (A : B = 2 : 1), let (A =2) and (B = k)
From (A : C = 1 : 3), let (A = c) and (C = 3c)
Secondly, make (A) the same in both expressions:
Set (2k = c), then (C = 3(2k) = 6k)
Thirdly, combine and simplify the ratios:
(A = 2k), (B =k), (C = 6k)
Thus, (A : B : C = 2k : k : 6k = 2 : 1 : 6)
Therefore, (A : B : C = 2 : 1 : 6)
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