Krishna has some hens and some goats. If the total number of animal heads are 81 and total number of animal legs are 234, how many goats does Krishna has?

Options

A. 45
B. 24
C. 36
D. None of these

Answer

To solve the problem, we will set up equations based on the information given about the number of heads and legs of the animals.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( H \) be the number of hens and \( G \) be the number of goats.

2. **Set Up the First Equation**:
Since each animal has one head, the total number of heads (hens + goats) is given as 81. Therefore, we can write:
\[ H + G = 81 \quad \text{(Equation 1)} \]

3. **Set Up the Second Equation**:
Hens have 2 legs each and goats have 4 legs each. The total number of legs is given as 234. Thus, we can write:
\[ 2H + 4G = 234 \quad \text{(Equation 2)} \]

4. **Simplify the Second Equation**:
We can simplify Equation 2 by dividing all terms by 2:
\[ H + 2G = 117 \quad \text{(Equation 3)} \]

5. **Subtract Equation 1 from Equation 3**:
Now we will subtract Equation 1 from Equation 3 to eliminate \( H \):
\[ (H + 2G) - (H + G) = 117 - 81 \]
This simplifies to:
\[ G = 36 \]

6. **Conclusion**:
Therefore, the number of goats \( G \) that Krishna has is:
\[ \text{Number of goats} = 36 \]

### Final Answer:
Krishna has 36 goats.