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 $: \text{D}$