Discussion
The ratio of spirit and water in solutions A and B is 2 : 3 and 7 : 8, respectively. Six litres of A are mixed with 9 litres of B. What is the percentage of spirit in the resulting mixture?
Answer: B
The mixture has 44 % spirit. Solution A has spirit and water in the ratio 2 : 3, so 6 litres of A contain 6 x 2/5 = 2.4 litres of spirit. Solution B has the ratio 7 : 8, so 9 litres of B contain 9 x 7/15 = 4.2 litres of spirit.
\[ \text{Spirit} = 2.4 + 4.2 = 6.6 \text{ litres} \]
\[ \text{Mixture} = 6 + 9 = 15 \text{ litres} \]
\[ \frac{6.6}{15} \times 100 = 44\% \]
The options 40 %, 52 % and 56 % are not the share of 6.6 litres in the 15 litres of the mixture. As a check, the water in the mixture is 3.6 + 4.8 = 8.4 litres, and 6.6 + 8.4 = 15 litres, the volume of the mixture.
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