One mixture contains wine and water in the ratio 3 : 2 and another contains them in the ratio 4 : 5. How many litres of the second mixture must be mixed with 3 litres of the first mixture so that the resulting mixture contains equal quantities of wine and water?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(5\frac{2}{5}\) litres
The first mixture has more wine than water and the second has more water than wine, so the extra water of the second must cancel the extra wine of the first.
3 litres of the first: wine \(\displaystyle =\frac{3}{5}\times3=1.8\), water \(=1.2\); extra wine \(=0.6\) litre
\(x\) litres of the second: wine \(\displaystyle =\frac{4x}{9}\), water \(\displaystyle =\frac{5x}{9}\); extra water \(\displaystyle =\frac{x}{9}\)
Equal quantities: \(\displaystyle \frac{x}{9}=0.6\)
\(\displaystyle x=5.4=5\frac{2}{5}\) litres
\(5\frac{2}{5}\) litres of the second mixture are needed.