Discussion
A solution of honey and water is 28 litres, with honey and water in the ratio 4 : 3. To this a 21 litre honey–water solution is added that has honey to water in the ratio 2 : 1. Again a 51 litre honey–water solution with honey to water in the ratio 9 : 8 is added. After this, 10 litres of the solution is replaced with pure honey. What is the final ratio of water to honey?
Answer: D
Convert each solution to litres of honey and water.
\[ 28 \text{ L at } 4:3 \rightarrow 16 \text{ honey}, \ 12 \text{ water} \]
\[ 21 \text{ L at } 2:1 \rightarrow 14 \text{ honey}, \ 7 \text{ water} \]
\[ 51 \text{ L at } 9:8 \rightarrow 27 \text{ honey}, \ 24 \text{ water} \]
\[ \text{total: } 100 \text{ L}, \ 57 \text{ honey}, \ 43 \text{ water} \]
Removing 10 L takes away 10% of each, then 10 L of pure honey is added:
\[ \text{honey} = 0.9(57) + 10 = 61.3, \qquad \text{water} = 0.9(43) = 38.7 \]
\[ \text{water} : \text{honey} = 387 : 613 \]
The convenient total of exactly 100 L makes the 10% removal easy to apply.
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