Bhuvan has some hens and some cows.if the total number of animal heads are 71 and the total number of feet are 228 how many hens does bhuvan have?

Options

A. 43
B. 32
C. 24
D. none of these

Answer

To solve the problem step by step, we will use algebra to find the number of hens Bhuvan has.

### Step 1: Define Variables
Let:
- \( H \) = number of hens
- \( C \) = number of cows

### Step 2: Set Up Equations
From the problem, we know:
1. The total number of animal heads (hens + cows) is 71:
\[ H + C = 71 \quad \text{(Equation 1)} \]
2. The total number of feet is 228. Since each hen has 2 feet and each cow has 4 feet:
\[ 2H + 4C = 228 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing the entire equation by 2:
\[ H + 2C = 114 \quad \text{(Equation 3)} \]

### Step 4: Solve for C in Terms of H
From Equation 1, we can express \( C \) in terms of \( H \):
\[ C = 71 - H \quad \text{(Substituting into Equation 1)} \]

### Step 5: Substitute C in Equation 3
Now, substitute \( C \) from Equation 1 into Equation 3:
\[ H + 2(71 - H) = 114 \]

### Step 6: Expand and Combine Like Terms
Expanding the equation:
\[ H + 142 - 2H = 114 \]
Combine like terms:
\[ 142 - H = 114 \]

### Step 7: Solve for H
Now, isolate \( H \):
\[ -H = 114 - 142 \]
\[ -H = -28 \]
\[ H = 28 \]

### Step 8: Conclusion
Thus, the number of hens Bhuvan has is:
\[ \boxed{28} \]

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