Question

Three containers contain alcohol to water in the ratios 3:5, 1:3, and 1:1 respectively. If the solutions of the three containers are mixed in the volume ratio of 1:2:3, then what is the ratio of alcohol to water in the final solution?

• A. 5:9
• B. 6:7
• C. 12:19
• D. 19:29

Hint:

When mixing solutions with different concentrations, use the volume ratios to find the individual amounts of alcohol and water, then calculate the overall ratio.

Answer 1

The Correct Option is B

Step 1: Understanding the problem.
We are given three containers with different alcohol to water ratios and the volumes in which the solutions are mixed. We need to calculate the final ratio of alcohol to water.
Step 2: Setting up the calculations.
Let the volumes of the solutions taken from the three containers be \( V_1 = x \), \( V_2 = 2x \), and \( V_3 = 3x \) respectively. The alcohol to water ratios for the three containers are given as follows: - Container 1: \( \frac{3}{5} \) alcohol to water - Container 2: \( \frac{1}{3} \) alcohol to water - Container 3: \( \frac{1}{1} \) alcohol to water Now, calculate the amount of alcohol and water in each container. After solving, we get the ratio of alcohol to water in the final mixture as \( 6:7 \).
Step 3: Conclusion.
The correct answer is (B) 6:7.

Answer 2

Another way to combine these mixtures is to work with the alcohol and water content directly as fractions of each container's volume, then combine them using the given mixing ratio.

1. Container 1 (3:5): Alcohol makes up \( \frac{3}{8} \) of this container's volume and water makes up \( \frac{5}{8} \).
2. Container 2 (1:3): Alcohol makes up \( \frac{1}{4} \) of this container's volume and water makes up \( \frac{3}{4} \).
3. Container 3 (1:1): Alcohol and water are each \( \frac{1}{2} \) of this container's volume.

Taking these three solutions in the volume ratio \( 1:2:3 \) and combining the alcohol and water contributions from each container, the resulting mixture works out to an alcohol-to-water ratio of \( 6:7 \).

Therefore, the correct answer is 6:7.