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 ?

Question

Accepted Answer

To solve the problem of determining how many peacocks are in the zoo, we need to use the information provided about the total number of heads and legs.

1. **Understanding the Problem:**
   - There are a total of 80 heads. Since each animal (deer or peacock) has one head, this means there are 80 animals in total.
   - The total number of legs is 200. Deer have 4 legs each, and peacocks have 2 legs each.

2. **Setting Up Equations:**
   - Let the number of deer be $ D $.
   - Let the number of peacocks be $ P $.
   - From the problem, we have two equations:
     1. $ D + P = 80 $ (since there are 80 heads)
     2. $ 4D + 2P = 200 $ (since there are 200 legs)

3. **Solving the Equations:**
   - From the first equation, express $ D $ in terms of $ P $:
     $$
     D = 80 - P
     $$
   - Substitute $ D = 80 - P $ into the second equation:
     $$
     4(80 - P) + 2P = 200
     $$
   - Simplify and solve for $ P $:
     $$
     320 - 4P + 2P = 200
     $$
     $$
     320 - 2P = 200
     $$
     $$
     2P = 120
     $$
     $$
     P = 60
     $$

4. **Conclusion:**
   - Therefore, the number of peacocks is 60, which corresponds to Option 4.

5. **Explanation of Incorrect Options:**
   - **Option 1 (20 peacocks):** If there were 20 peacocks, then there would be 60 deer (since $ 80 - 20 = 60 $). This would result in $ 4 \times 60 + 2 \times 20 = 240 + 40 = 280 $ legs, which is incorrect.
   - **Option 2 (40 peacocks):** If there were 40 peacocks, then there would be 40 deer. This would result in $ 4 \times 40 + 2 \times 40 = 160 + 80 = 240 $ legs, which is incorrect.
   - **Option 3 (52 peacocks):** If there were 52 peacocks, then there would be 28 deer. This would result in $ 4 \times 28 + 2 \times 52 = 112 + 104 = 216 $ legs, which is incorrect.

By following the logical steps and calculations, we confirm that Option 4 is indeed the correct answer, with 60 peacocks in the zoo.