In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?

We combine everything into the bowl:

$\text{Orange Juice} = 60 \text{ ml}, \quad \text{Water} = 40 \text{ ml}, \quad \text{Apple Juice} = 100 \text{ ml}$

$\text{Total fruit punch} = 60 + 40 + 100 = 200 \text{ ml}$

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Since the punch is well mixed, each component exists in a fixed proportion:

$\text{Orange Juice} = \dfrac{60}{200} = \dfrac{3}{10}$

$\text{Water} = \dfrac{40}{200} = \dfrac{2}{10}$

$\text{Apple Juice} = \dfrac{100}{200} = \dfrac{5}{10}$

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When Madhu drinks $50$ ml of the well-mixed punch, she doesn't drink only one component — she drinks the mixture. So each component is removed in the same proportion as it exists in the punch.

$\text{OJ removed} = \dfrac{3}{10} \times 50 = 15 \text{ ml}$

$\text{Water removed} = \dfrac{2}{10} \times 50 = 10 \text{ ml}$

$\text{Apple Juice removed} = \dfrac{5}{10} \times 50 = 25 \text{ ml}$

Remaining in the bowl:

$\text{OJ} = 60 - 15 = 45 \text{ ml}$

$\text{Water} = 40 - 10 = 30 \text{ ml}$

$\text{Apple} = 100 - 25 = 75 \text{ ml}$

$\text{Total remaining} = 45 + 30 + 75 = 150 \text{ ml}$

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Let $x$ be the ml of orange juice to be added. We need orange juice to be $50\%$ of the new total:

$45 + x = 50\% \text{ of } (150 + x)$

$45 + x = \dfrac{1}{2}(150 + x)$

Multiply both sides by $2$ to remove the fraction:

$90 + 2x = 150 + x$

$2x - x = 150 - 90$

$x = 60$

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Verification: After adding $60$ ml of OJ, total OJ $= 45 + 60 = 105$ ml and total punch $= 150 + 60 = 210$ ml.

$\dfrac{105}{210} = \dfrac{1}{2} = 50\%$ ✓

$\boxed{60 \text{ ml of orange juice should be added.}}$