Directions: Solve the question below.

Three containers whose capacities are in the ratio of 1:2:3 are filled with a mixture of fruit concentrate and water. The ratio of concentrate to water in the first, second, and third containers is 3:1, 1:1, and 2:1, respectively. If the contents of all three containers are combined in a larger container, what will be the ratio of concentrate to water in the resulting mixture?

The correct option is 5:3.

Step 1: Understand the capacities and mixture ratios of the containers.

Let the capacities of the three containers be in the ratio 1 : 2 : 3.

The ratio of concentrate to water in each container is given as follows:

• Container 1: Concentrate : Water = 3 : 1 (Total parts = 3 + 1 = 4)

• Container 2: Concentrate : Water = 1 : 1 (Total parts = 1 + 1 = 2)

• Container 3: Concentrate : Water = 2 : 1 (Total parts = 2 + 1 = 3)

Step 2: Choose suitable capacities to simplify calculations.

To avoid working with fractions, find the Least Common Multiple (LCM) of the total ratio parts (4, 2, and 3):

$\text{LCM}(4,2,3)=12$

Assuming 1 unit of the capacity ratio corresponds to 12 volume units, the capacities of the three containers are:

• Container 1 capacity = 1 × 12 = 12 units

• Container 2 capacity = 2 × 12 = 24 units

• Container 3 capacity = 3 × 12 = 36 units

Step 3: Calculate the volume of concentrate and water in each container.

For Container 1 (Total volume = 12 units):

$\text{Concentrate}=\frac{3}{4}\times 12=9\text{units}$

$\text{Water}=\frac{1}{4}\times 12=3\text{units}$

For Container 2 (Total volume = 24 units):

$\text{Concentrate}=\frac{1}{2}\times 24=12\text{units}$

$\text{Water}=\frac{1}{2}\times 24=12\text{units}$

For Container 3 (Total volume = 36 units):

$\text{Concentrate}=\frac{2}{3}\times 36=24\text{units}$

$\text{Water}=\frac{1}{3}\times 36=12\text{units}$

Step 4: Find the total concentrate and total water in the combined mixture.

$\text{Total Concentrate}=9+12+24=45\text{units}$

$\text{Total Water}=3+12+12=27\text{units}$

Step 5: Calculate the ratio of concentrate to water in the resulting mixture.

$\text{Ratio}=\frac{\text{Total Concentrate}}{\text{Total Water}}=\frac{45}{27}=\frac{5}{3}$

Thus, the ratio of concentrate to water in the combined mixture is 5:3.