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 two-variable linear equation problem based on counting heads and legs of two different animals. Step 1:Define variables.
Let number of deer = x (4 legs each)
Let number of peacocks = y (2 legs each)
Step 2:Form equations.
\[ x + y = 80 \quad \cdots (1) \] \[ 4x + 2y = 200 \quad \cdots (2) \]
Step 3:Eliminate one variable.
Multiply equation (1) by 2: \[ 2x + 2y = 160 \] Subtracting 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:Check consistency.
\[ x = 20,\; y = 60 \] Verify: \[ 20 + 60 = 80,\quad 4(20) + 2(60) = 80 + 120 = 200 \]
Final Answer: 60