Question : If $a: b=3: 7$, then $(2 a+3 b):(3 a+2 b)$ is:
Option 1: $27:23$
Option 2: $23:29$
Option 3: $21:29$
Option 4: $21:23$
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Correct Answer: $27:23$
Solution :
Given $a:b=3:7$
Let $a=3k$ and $b=7k$ for some constant $k$.
Now, $(2 a+3 b):(3 a+2 b)$
$=\{2(3k)+3(7k)\}:\{3(3k)+2(7k)\}$
$=(6k+21k):(9k+14k)$
$=27k:23k$
$=27:23$
Hence, the correct answer is $27:23$.
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