Let:

• $x$ be the amount of mango juice (in liters) to be added to the 1 liter of drink.

Currently, the drink contains:

• 10% mango juice, so $0.1$ liters of mango juice.

After adding $x$ liters of pure mango juice, the total volume of the mixture will be:

• $1 + x$ liters.

We want the mango juice to make up 40% of the total volume. This leads to the equation:

$\frac{0.1 + x}{1 + x} = 0.4$

To solve for $x$:

1. Multiply both sides by $1 + x$:

   $0.1 + x = 0.4(1 + x)$

2. Expand and simplify:

   $0.1 + x = 0.4 + 0.4x$

3. Move all terms involving $x$ to one side:

   $x - 0.4x = 0.4 - 0.1$

   $0.6x = 0.3$

4. Divide by $0.6$:

   $x = \frac{0.3}{0.6} = 0.5$

Thus, 0.5 liters of pure mango juice needs to be added to achieve 40% mango juice in the mixture.

Would you like further clarification, or do you have more questions?

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Here are 5 related questions:

1. How would the calculation change if we wanted 50% mango juice in the mixture?
2. What if the initial drink had only 5% mango juice?
3. How can we find the percentage if we added 1 liter of mango juice instead?
4. What if we started with 2 liters of the initial 10% juice drink?
5. How does this relate to problems involving ratios and percentages in mixtures?

Tip: For mixture problems, setting up equations based on percentages helps ensure accurate results.