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Let a person have $₹ \; 100.$

He can buy $50$ oranges or $40$ mangoes.

- Price of each orange $ = \frac{100}{50} = 2$
- Price of each mango $ = \frac{100}{40} = \frac{5}{2}$

He retains $10\%$ of the amount for the amount for taxi fares, then remaining amount $ = 100 – 10 = ₹ \; 90$

He buys $20$ mangoes. The price of $20$ mangoes $ = 20 \times \frac{5}{2} = ₹ \; 50$

Remaining amount $ = 90 – 50 = ₹ \; 40$

He purchases oranges from the remaining amount.

$\therefore$ The number of oranges he can purchase $ = \frac{40}{2} = 20$ oranges.

Correct Answer $: \text{D}$