Question : If $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}$, what is the value of ratio $(C+A)^{2}:(A+B)^{2}:(B+C)^{2}$?
Option 1: $9:4:25$
Option 2: $25:4:9$
Option 3: $64:25:49$
Option 4: $49:25:64$
Correct Answer: $64:25:49$
Solution :
Given: $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}$
Let $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}=k$
$⇒A=3k,B=2k,C=5k$
Putting these values, we get,
$(C+A)^{2}:(A+B)^{2}:(B+C)^{2}$
$=(5k+3k)^{2}:(3k+2k)^{2}:(2k+5k)^{2}$
$=64k^{2}:25k^{2}:49k^{2}$
$=64:25:49$
Hence, the correct answer is $64:25:49$.
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