There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?

Options

A. A) 50
B. B) 30
C. C) 60
D. D) 20

Explanation

To solve the problem of finding the number of peacocks in the zoo, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let \( D \) be the number of deer and \( P \) be the number of peacocks.

2. **Set Up the Equations**:
From the problem, we know:
- The total number of heads (deer + peacocks) is 80:
\[ D + P = 80 \quad \text{(Equation 1)} \]
- The total number of legs (deer have 4 legs and peacocks have 2 legs) is 200:
\[ 4D + 2P = 200 \quad \text{(Equation 2)} \]

3. **Rearrange Equation 1**:
From Equation 1, we can express \( P \) in terms of \( D \):
\[ P = 80 - D \quad \text{(Equation 3)} \]

4. **Substitute Equation 3 into Equation 2**:
Substitute \( P \) from Equation 3 into Equation 2:
\[ 4D + 2(80 - D) = 200 \]

5. **Simplify the Equation**:
Expand and simplify:
\[ 4D + 160 - 2D = 200 \]
Combine like terms:
\[ 2D + 160 = 200 \]

6. **Isolate \( D \)**:
Subtract 160 from both sides:
\[ 2D = 200 - 160 \]
\[ 2D = 40 \]
Divide by 2:
\[ D = 20 \]

7. **Find \( P \)**:
Substitute \( D \) back into Equation 3 to find \( P \):
\[ P = 80 - D = 80 - 20 = 60 \]

8. **Conclusion**:
Therefore, the number of peacocks is:
\[ \boxed{60} \]