Question : If $B:A = 2:3$ and $A:C = 5:7$, then what is $(A + B):(B + C)$?
Option 1: $25:26$
Option 2: $25:36$
Option 3: $25:31$
Option 4: $27:43$
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Correct Answer: $25:31$
Solution :
$B:A = 2:3$ -----------(1)
$A:C = 5:7$ -----------(2)
Multiply equation (1) by 5 and equation (2) by 3, we have:
$B:A = 10:15$
$A:C = 15:21$
⇒ $B:A: C = 10:15:21$
Let $B=10k,A=15k,$ and $C=21k$
So, $(A + B):(B + C) = (15k + 10k):(10k + 21k) = 25k:31k=25:31$
Hence, the correct answer is $25:31$.
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