In a mixture of juice and water, juice is 20% more than water. This is mixed with another mixture having juice & water in ratio 5:6. If these two are mixed in ratio 3:4. Find ratio of juice & water in final mixture.

Options

A. `35:39`
B. `35:38`
C. `1:1`
D. `38:39`

Answer

To solve the problem, we need to find the ratio of juice and water in the final mixture after mixing two different mixtures. Let's break it down step by step.

### Step 1: Analyze the First Mixture
In the first mixture, juice is 20% more than water.

- Let the amount of water be \( W \).
- Therefore, the amount of juice will be \( J = W + 0.2W = 1.2W \).

Now, we can express the ratio of juice to water in the first mixture:

\[ \text{Ratio of Juice to Water in Mixture 1} = \frac{J}{W} = \frac{1.2W}{W} = 1.2:1 \]

To express this in simpler terms, we can multiply both sides by 10 to avoid decimals:

\[ \text{Ratio of Juice to Water in Mixture 1} = 12:10 \quad \text{or} \quad 6:5 \]

### Step 2: Analyze the Second Mixture
In the second mixture, the ratio of juice to water is given as 5:6.

- Let the amount of juice be \( J_2 = 5x \) and the amount of water be \( W_2 = 6x \) for some \( x \).

### Step 3: Combine the Two Mixtures
The two mixtures are mixed in the ratio of 3:4.

Let’s denote the quantities of the first and second mixtures as \( 3k \) and \( 4k \) respectively, where \( k \) is a common multiplier.

- For the first mixture (3 parts):
- Juice: \( \frac{6}{11} \times 3k = \frac{18k}{11} \)
- Water: \( \frac{5}{11} \times 3k = \frac{15k}{11} \)

- For the second mixture (4 parts):
- Juice: \( \frac{5}{11} \times 4k = \frac{20k}{11} \)
- Water: \( \frac{6}{11} \times 4k = \frac{24k}{11} \)

### Step 4: Calculate Total Juice and Water in the Final Mixture
Now, we can find the total amount of juice and water in the final mixture:

- Total Juice:
\[ \text{Total Juice} = \frac{18k}{11} + \frac{20k}{11} = \frac{38k}{11} \]

- Total Water:
\[ \text{Total Water} = \frac{15k}{11} + \frac{24k}{11} = \frac{39k}{11} \]

### Step 5: Find the Ratio of Juice to Water in the Final Mixture
Now we can find the ratio of juice to water in the final mixture:

\[ \text{Ratio of Juice to Water} = \frac{\frac{38k}{11}}{\frac{39k}{11}} = \frac{38}{39} \]

Thus, the final ratio of juice to water in the mixture is:

\[ \text{Final Ratio} = 38:39 \]