Two syrups

There are two pots of mixture of syrup and water having ratios 3:2 & 4:5 respectively. What quantity of solution of 1st pot is to be mixed with 3 litre of 2nd pot to get a new mixture where both syrup and water will be same?

Final Answer:

V₁ =  5/3 = 1 ²⁄₃ l

Step-by-step explanation:

$$\begin{gathered} V_2=3\text{l} \\ {r}_1=3:2 \\ {r}_2=4:5 \\ S=W \\ {S}_1=\frac{3}{3+2}\cdot V_1 \\ {S}_2=\frac{4}{4+5}\cdot V_2 \\ \frac{3}{5}\cdot V_1+\frac{4}{9}\cdot V_2=\frac{V_1+V_2}{2} \\ \frac{3}{5}\cdot V_1+\frac{4}{9}\cdot 3=\frac{V_1+3}{2} \\ 3/5\cdot V_1+4/9\cdot 3=(V_1+3)/2 \\ 9V_1=15 \\ {V}_1=\frac{15}{9}=1.66666667 \\ {V}_1=\frac{5}{3}\doteq 1.666667=\frac{5}{3}\text{l}=1.6667\text{l} \end{gathered}$$

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