Glass 'A' contains 400 ml sprite & glass 'B' contains 220 ml coke. 4X ml sprite taken out from 'A' and mixed in 'B' and then 3X ml mixture from 'B' taken out and poured into a vacant glass 'C'. If ratio of coke to sprite in glass C is 11 : 4, then find remaining quantity of sprite in glass 'B'?

Options

A. 240 ml
B. 60 ml
C. 64 ml
D. 80 ml

Answer

To solve the problem step by step, we will analyze the situation involving the two glasses and the mixtures.

### Step 1: Understand the initial quantities
- Glass A contains **400 ml of Sprite**.
- Glass B contains **220 ml of Coke**.

### Step 2: Determine the amount of Sprite transferred to Glass B
- We take out **4X ml of Sprite** from Glass A and mix it into Glass B.
- After this transfer, the amount of Sprite in Glass A becomes **400 - 4X ml**.
- The total volume in Glass B becomes **220 ml of Coke + 4X ml of Sprite = (220 + 4X) ml**.

### Step 3: Determine the composition of the mixture in Glass B
- In Glass B, after adding the Sprite, we have:
- Coke: **220 ml**
- Sprite: **4X ml**

### Step 4: Calculate the ratio of Coke to Sprite in Glass B
- The ratio of Coke to Sprite in Glass B is:
\[ \text{Ratio} = \frac{\text{Coke}}{\text{Sprite}} = \frac{220}{4X} \]

### Step 5: Determine the amount of mixture taken from Glass B to Glass C
- We take out **3X ml of the mixture** from Glass B and pour it into Glass C.
- The total mixture in Glass B is **(220 + 4X) ml**.
- The fraction of the mixture taken out is:
\[ \frac{3X}{220 + 4X} \]

### Step 6: Calculate the amount of Coke and Sprite in the mixture transferred to Glass C
- Amount of Coke in the mixture taken out:
\[ \text{Coke in C} = 220 \times \frac{3X}{220 + 4X} \]
- Amount of Sprite in the mixture taken out:
\[ \text{Sprite in C} = 4X \times \frac{3X}{220 + 4X} \]

### Step 7: Set up the ratio of Coke to Sprite in Glass C
- We know the ratio of Coke to Sprite in Glass C is given as **11:4**.
- Therefore, we can set up the equation:
\[ \frac{220 \times \frac{3X}{220 + 4X}}{4X \times \frac{3X}{220 + 4X}} = \frac{11}{4} \]
- Simplifying this gives:
\[ \frac{220}{4X} = \frac{11}{4} \]

### Step 8: Solve for X
- Cross-multiplying gives:
\[ 220 \times 4 = 11 \times 4X \]
\[ 880 = 44X \]
\[ X = 20 \]

### Step 9: Find the remaining quantity of Sprite in Glass B
- The amount of Sprite taken out from Glass A is:
\[ 4X = 4 \times 20 = 80 \text{ ml} \]
- The remaining amount of Sprite in Glass A is:
\[ 400 - 80 = 320 \text{ ml} \]
- The amount of Sprite in Glass B after the transfer is:
\[ 4X = 80 \text{ ml} \]
- Therefore, the remaining quantity of Sprite in Glass B is:
\[ 80 \text{ ml} \]

### Final Answer:
The remaining quantity of Sprite in Glass B is **80 ml**.

---