Let’s analyze the problem step by step.

1. Initial Volumes:

   • Glass A: 400 ml of Sprite
   • Glass B: 220 ml of Coke

2. Transferring Sprite:

   • After transferring $4X$ ml of Sprite from Glass A to Glass B:
     • Sprite in Glass A: $400 - 4X$ ml
     • Coke in Glass B: 220 ml
     • Sprite in Glass B: $4X$ ml
     • Total mixture in Glass B = $220 + 4X$ ml

3. Taking out the mixture:

   • When $3Y$ ml of the mixture is taken out from Glass B, the composition of the mixture is:
     • Coke: $\frac{220}{220 + 4X} \cdot 3Y$
     • Sprite: $\frac{4X}{220 + 4X} \cdot 3Y$

4. Remaining amounts after removing the mixture:

   • Remaining Coke in Glass B: $220 - \frac{220}{220 + 4X} \cdot 3Y$
   • Remaining Sprite in Glass B: $4X - \frac{4X}{220 + 4X} \cdot 3Y$

5. Setting up the ratio:

   • According to the problem, the resulting ratio of Coke to Sprite in the mixture from Glass B is $11:4$. This gives us the equation: $\frac{220 - \frac{220 \cdot 3Y}{220 + 4X}}{4X - \frac{4X \cdot 3Y}{220 + 4X}} = \frac{11}{4}$

6. Cross-multiplying to eliminate the fraction: $4 \left( 220 - \frac{220 \cdot 3Y}{220 + 4X} \right) = 11 \left( 4X - \frac{4X \cdot 3Y}{220 + 4X} \right)$

7. Solving for $X$ and $Y$: Simplifying this equation will help in determining values for $X$ and $Y$, which can be substituted back to find how much Sprite remains in Glass B.

Remaining Sprite Calculation

To find the remaining Sprite in Glass B, we can set up the equation as derived from the last step. However, since $X$ and $Y$ are unknown, we might need additional information to solve the problem fully or to define those variables.

Would you like to provide specific values for $X$ and $Y$, or should we proceed with further simplification?

Follow-up Questions:

1. What values do you want to assign to $X$ and $Y$?
2. Would you like to see a detailed breakdown of the cross-multiplication step?
3. Are you interested in understanding how to derive these equations from the problem statement?
4. Do you want to explore a similar problem for practice?
5. Would you like to know how ratios work in mixtures in general?

Tip: Always keep track of the initial volumes and any transfers to help in setting up the equations correctly.