In a group of equal number of cows and herdsmen the number of legs was 28 less than four times the number of heads. The number of herdsmen was `(A) 7` `(B) 28` `(C) 21` `(D) 14`

Options

A. 7
B. 28
C. 21
D. 14

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let:
- \( A \) = number of cows
- \( B \) = number of herdsmen

Since the problem states that the number of cows and herdsmen is equal, we can say:
\[ A = B \]

### Step 2: Calculate Total Heads
Each cow and each herdsman has one head. Therefore, the total number of heads \( H \) is:
\[ H = A + B = A + A = 2A \]

### Step 3: Calculate Total Legs
Each cow has 4 legs and each herdsman has 2 legs. Therefore, the total number of legs \( L \) is:
\[ L = 4A + 2B \]

Since \( A = B \), we can substitute \( B \) with \( A \):
\[ L = 4A + 2A = 6A \]

### Step 4: Set Up the Equation
According to the problem, the number of legs is 28 less than four times the number of heads. This can be expressed as:
\[ L = 4H - 28 \]

Substituting the expressions for \( L \) and \( H \):
\[ 6A = 4(2A) - 28 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ 6A = 8A - 28 \]

### Step 6: Rearrange the Equation
Rearranging gives:
\[ 6A - 8A = -28 \]
\[ -2A = -28 \]

### Step 7: Solve for \( A \)
Dividing both sides by -2:
\[ A = 14 \]

### Step 8: Find Number of Herdsmen
Since \( A = B \), the number of herdsmen \( B \) is:
\[ B = 14 \]

### Conclusion
The number of herdsmen is \( 14 \).