In a mixture of juice & water, 40 litres water is mixed due to which ratio changes from 3:4 to 1: 4. Find initial quantity of mixture. (in litres)

Options

A. A)45
B. B)25
C. C)30
D. D)35

Answer

To solve the problem, we need to determine the initial quantity of the mixture of juice and water before 40 liters of water was added, which changed the ratio from 3:4 to 1:4.

### Step-by-Step Solution:

1. **Understand the Initial and Final Ratios**:
- The initial ratio of juice to water is 3:4.
- The final ratio of juice to water after adding 40 liters of water is 1:4.

2. **Express the Initial Quantities**:
- Let the initial quantities of juice and water be represented as:
- Juice = 3x
- Water = 4x
- Here, x is a common multiplier.

3. **Calculate the Final Quantities After Adding Water**:
- After adding 40 liters of water, the new quantity of water becomes:
- Water = 4x + 40

4. **Set Up the Final Ratio**:
- According to the final ratio (juice:water = 1:4), we can express this as:
\[ \frac{3x}{4x + 40} = \frac{1}{4} \]

5. **Cross Multiply to Solve for x**:
- Cross multiplying gives us:
\[ 3x \cdot 4 = 1 \cdot (4x + 40) \]
- Simplifying this:
\[ 12x = 4x + 40 \]

6. **Isolate x**:
- Rearranging the equation:
\[ 12x - 4x = 40 \]
\[ 8x = 40 \]
\[ x = 5 \]

7. **Calculate the Initial Quantities**:
- Now that we have the value of x, we can find the initial quantities:
- Juice = 3x = 3(5) = 15 liters
- Water = 4x = 4(5) = 20 liters

8. **Find the Initial Quantity of the Mixture**:
- The total initial quantity of the mixture is:
\[ \text{Total Mixture} = \text{Juice} + \text{Water} = 15 + 20 = 35 \text{ liters} \]

### Final Answer:
The initial quantity of the mixture is **35 liters**.

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