Ratio of acid and water

In a mixture of 60 litres, the ratio of acid to water is 2:1. If the ratio of acid to water is to be changed to 1:2, how much water must be added?

Final Answer:

W =  60 l

Step-by-step explanation:

$$\begin{gathered} V=60\text{l} \\ {r}_1=2:1=2 \\ {r}_2=1:2=0.5 \\ x:(V-x)=r_1=x:y \\ x=r_1\cdot (V-x) \\ x=2\cdot (60-x) \\ 3x=120 \\ x=\frac{120}{3}=40 \\ x=40 \\ y=V-x=60-40=20\text{l} \\ x:(W+y)=r_2 \\ x=r_2\cdot (W+y) \\ 40=0.5\cdot (W+20) \\ 0.5W=30 \\ W=\frac{30}{0.5}=60 \\ W=60=60\text{l} \end{gathered}$$

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