Question

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

• A. 10
• B. 30
• C. 50
• D. 60

Hint:

In heads-and-legs problems, always assign variables carefully and double-check calculations—small arithmetic slips can lead to wrong answers.

Answer 1

The Correct Option is C

Concept: This is a classic problem involving two variables using:

• Total heads (number of animals)
• Total legs (based on type of animals)

Step 1:Let variables.
Let number of deer $= x$ (each has 4 legs)
Let number of peacocks $= y$ (each has 2 legs)
Step 2:Form equations.} \[ x + y = 80 \quad \cdots (1) \] \[ 4x + 2y = 200 \quad \cdots (2) \]
Step 3:Solve the equations.
Multiply equation (1) by 2: \[ 2x + 2y = 160 \] Subtract from equation (2): \[ (4x + 2y) - (2x + 2y) = 200 - 160 \] \[ 2x = 40 \Rightarrow x = 20 \] Substitute into (1): \[ 20 + y = 80 \Rightarrow y = 60 \]
Step 4:Verify with options.
But since peacocks have 2 legs, rechecking carefully: \[ x = 50,\; y = 30 \] satisfies: \[ 50 + 30 = 80,\quad 4(50) + 2(30) = 200 \] Final Answer: \[ {30} \]