There are some shepherds and their sheep in a grazing field. The no. of total heads are 60 and total legs are 168 including both men and sheep. The no. of sheep is:

Options

A. 18
B. 16
C. 24
D. 36

Answer

To solve the problem of finding the number of sheep in the grazing field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem:**
- We have a total of 60 heads (which means 60 animals in total, including both shepherds and sheep).
- We have a total of 168 legs.

2. **Set Up the Variables:**
- Let \( S \) be the number of sheep.
- Let \( H \) be the number of shepherds (or men).

3. **Create the Equations:**
- From the total number of heads, we can write the first equation:
\[ S + H = 60 \quad \text{(1)} \]
- From the total number of legs, we know that each shepherd has 2 legs and each sheep has 4 legs. Therefore, we can write the second equation:
\[ 4S + 2H = 168 \quad \text{(2)} \]

4. **Solve the First Equation for \( H \):**
- Rearranging equation (1):
\[ H = 60 - S \quad \text{(3)} \]

5. **Substitute \( H \) in the Second Equation:**
- Substitute equation (3) into equation (2):
\[ 4S + 2(60 - S) = 168 \]
- Simplifying this gives:
\[ 4S + 120 - 2S = 168 \]
\[ 2S + 120 = 168 \]

6. **Isolate \( S \):**
- Subtract 120 from both sides:
\[ 2S = 168 - 120 \]
\[ 2S = 48 \]
- Divide by 2:
\[ S = 24 \]

7. **Find the Number of Shepherds:**
- Substitute \( S \) back into equation (1) to find \( H \):
\[ H = 60 - 24 = 36 \]

8. **Conclusion:**
- The number of sheep is \( S = 24 \).

### Final Answer:
The number of sheep is **24**.