Two vessels A and B, each with the capacity of 8 litres, are full of solutions of acid and water. The ratio of acid and water in Vessel A is 3: 1 and that in the case of Vessel B i... Two vessels A and B, each with the capacity of 8 litres, are full of solutions of acid and water. The ratio of acid and water in Vessel A is 3: 1 and that in the case of Vessel B is 5: 3. Two litres of solution are taken out from B and added to A. After mixing thoroughly, 2 litres of solution are taken out from A and added to B. What is the ratio of acid and water in the final solution in B? Read more

Steps to Solve

1. Identify Initial Amounts in Each Vessel

Let's assume vessel A contains an initial amount of acid and water. For example, let there be $V_A$ total volume in vessel A consisting of $A_A$ amount of acid and $W_A$ amount of water.

Vessel B may have an initial total volume of $V_B$, consisting of $A_B$ amount of acid and $W_B$ amount of water.

2. Perform Transfers of Solutions

If you transfer a certain volume $x$ from vessel A to B, you will need to calculate what's inside that transferred volume. For instance, if vessel A has a concentration of acid $C_A = \frac{A_A}{V_A}$, then the amount of acid transferred to vessel B will be $C_A \cdot x$. The remaining amount of acid in vessel A is then $A_A - C_A \cdot x$.

3. Calculate New Amounts in Vessel B

After transferring the amount to vessel B, you'll need to add the transferred amounts to vessel B's existing amounts. Thus,

• New amount of acid in vessel B: ( A_B + C_A \cdot x )
• New amount of water in vessel B: ( W_B + (x - C_A \cdot x) )

Here, you also need to account for the dilution effect if your mixture becomes more water than acid.

4. Determine the Final Ratio

Finally, you can find the ratio of acid to water in vessel B using: $$ \text{Ratio} = \frac{A_B + C_A \cdot x}{W_B + (x - C_A \cdot x)} $$

5. Output the Final Result

Calculate the numerical values from the final formula to get the exact ratio of acid to water in vessel B.