In a farm there are goats and peacocks. If the number of heads are 60 and the number of feet are 170 , then the number of goats =?
A. 18
B. 20
C. 23
D. 25

Options

A. C
B. B
C. D
D. A

Answer

To solve the problem, we can use a system of equations based on the information given about the heads and feet of the animals on the farm.

### Step 1: Define Variables
Let:
- \( x \) = number of goats
- \( y \) = number of peacocks

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of heads (goats + peacocks) is 60:
\[ x + y = 60 \quad \text{(Equation 1)} \]

2. The total number of feet (goats have 4 feet and peacocks have 2 feet) is 170:
\[ 4x + 2y = 170 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 60 - x \]

### Step 4: Substitute \( y \) in Equation 2
Now we substitute \( y \) in Equation 2:
\[ 4x + 2(60 - x) = 170 \]

### Step 5: Simplify the Equation
Expanding the equation:
\[ 4x + 120 - 2x = 170 \]
Combining like terms:
\[ 2x + 120 = 170 \]

### Step 6: Isolate \( x \)
Subtract 120 from both sides:
\[ 2x = 50 \]
Now divide by 2:
\[ x = 25 \]

### Step 7: Conclusion
The number of goats is \( x = 25 \).

### Final Answer
Thus, the number of goats is **25** (Option D).

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