A monkey in Zoo becomes lucky if he eats three different fruits. What is the largest number of monkeys one can make lucky, by having $20$ oranges, $30$ bananas, $40$ peaches and $50$ tangerines? Justify your answer.

(A): $30$ (B): $35$ (C): $40$ (D): $45$ (E): None of the above.
To determine the largest number of monkeys that can be made lucky, we need to ensure that each monkey eats three different fruits. We have the following quantities of fruits:
- 20 oranges
- 30 bananas
- 40 peaches
- 50 tangerines

We need to maximize the number of monkeys that can eat three different fruits. Let's break down the steps:

1. **Initial Setup:**
   We start with:
   \[
   \text{Oranges} = 20, \quad \text{Bananas} = 30, \quad \text{Peaches} = 40, \quad \text{Tangerines} = 50
   \]

2. **First 10 Monkeys:**
   Each of these monkeys can eat one orange, one banana, and one peach:
   \[
   \text{Oranges} = 20 - 10 = 10, \quad \text{Bananas} = 30 - 10 = 20, \quad \text{Peaches} = 40 - 10 = 30, \quad \text{Tangerines} = 50
   \]
   Number of lucky monkeys so far: 10

3. **Next 10 Monkeys:**
   Each of these monkeys can eat one orange, one banana, and one tangerine:
   \[
   \text{Oranges} = 10 - 10 = 0, \quad \text{Bananas} = 20 - 10 = 10, \quad \text{Peaches} = 30, \quad \text{Tangerines} = 50 - 10 = 40
   \]
   Number of lucky monkeys so far: 20

4. **Next 10 Monkeys:**
   Each of these monkeys can eat one banana, one peach, and one tangerine:
   \[
   \text{Oranges} = 0, \quad \text{Bananas} = 10 - 10 = 0, \quad \text{Peaches} = 30 - 10 = 20, \quad \text{Tangerines} = 40 - 10 = 30
   \]
   Number of lucky monkeys so far: 30

5. **Next 10 Monkeys:**
   Each of these monkeys can eat one peach and two tangerines:
   \[
   \text{Oranges} = 0, \quad \text{Bananas} = 0, \quad \text{Peaches} = 20 - 10 = 10, \quad \text{Tangerines} = 30 - 10 = 20
   \]
   Number of lucky monkeys so far: 40

At this point, we have used up all the oranges and bananas, and we have 10 peaches and 20 tangerines left. However, we cannot make any more monkeys lucky because we need three different fruits for each monkey.

Therefore, the largest number of monkeys that can be made lucky is 40.

The final answer is $\boxed{40}$