Discussion
The ratio of spirit and water in solution A is 6 : 7 and the ratio of water and spirit in solution B is 9 : 4. 3 L of A is mixed with 5 L of B. In 780 mL of the resulting solution, what is the quantity (in mL) of spirit?
Answer: A
The spirit in 780 mL of the mixture is 285 mL. In solution A the spirit is \(\frac{6}{13}\), so 3 L has \(\frac{18}{13}\) L of spirit. In solution B the ratio of water to spirit is 9 : 4, so spirit is \(\frac{4}{13}\), and 5 L has \(\frac{20}{13}\) L. \[ \begin{aligned} \text{Spirit} &= \frac{18}{13} + \frac{20}{13} \\ &= \frac{38}{13}\text{ L} \end{aligned} \] \[ \text{Total} = 3 + 5 = 8\text{ L} \] \[ \begin{aligned} \text{Fraction of spirit} &= \frac{38}{13\times 8} \\ &= \frac{19}{52} \end{aligned} \] \[ 780\times\frac{19}{52} = 15\times 19 = 285\text{ mL} \] Reading B as spirit to water (4 : 9 swapped) would give a different value, so the order in the stem matters; 304, 270 and 266 do not result.
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