If the sum of 5% of \(x\) and 4% of \(y\) is \(\frac{2}{3}\) of the sum of 6% of \(x\) and 8% of \(y\), then the ratio of \(y\) to \(x\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 : 4
The condition is written as one equation in \(x\) and \(y\); collecting the \(x\) terms on one side and the \(y\) terms on the other gives the ratio.
\(\displaystyle\frac{5x}{100}+\frac{4y}{100}=\frac{2}{3}\left(\frac{6x}{100}+\frac{8y}{100}\right)\)
\(15x+12y=2(6x+8y)\)
\(15x+12y=12x+16y\)
\(3x=4y\)
\(\displaystyle\frac{y}{x}=\frac{3}{4}\), so \(y:x=3:4\)
Tip: The question asks for y to x; 4 : 3 (Option 1) is the ratio of \(x\) to \(y\).