Question : If A : B = $\frac{1}{2}:\frac{1}{3}$, B : C = $\frac{1}{5}:\frac{1}{3}$ ,then (A + B) : (B + C) is equal to:
Option 1: 5 : 8
Option 2: 9 : 10
Option 3: 15 : 16
Option 4: 6 : 15
Correct Answer: 15 : 16
Solution :
Given:
A : B = $\frac{1}{2}:\frac{1}{3}$
⇒ A : B = 3 : 2
B : C = $\frac{1}{5}:\frac{1}{3}$
⇒ B : C = 3 : 5
A : B = 3 : 2 is multiplied by 3 and B : C = 3 : 5 is multiplied by 2,
We get, A : B = 9 : 6 and B : C = 6 : 10
$\therefore$ A : B : C = 9 : 6 : 10
Let A = 9k, B = 6k, and C = 10k
So, (A + B) : (B + C) = (9k + 6k) : (6k + 10k) = 15k : 16k = 15 : 16
Hence, the correct answer is 15 : 16.
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