Discussion
If x : y = 3 : 4 then the value of (2x + 3y) : (3y - 2x) is
Answer: D
The ratio is 3:1.
Since \(x : y = 3 : 4\), put \(x = 3k\) and \(y = 4k\).
\[ \begin{aligned} 2x + 3y &= 6k + 12k = 18k \\ 3y - 2x &= 12k - 6k = 6k \\ 18k : 6k &= 3 : 1 \end{aligned} \]
1:3 is the ratio turned upside down, and 3:2 and 2:3 come from arithmetic slips in one of the two brackets.
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