p men can complete a piece of work in 60 days. Find the value of p
Statement 1: 30 men can complete the same work in 80 days.
Statement 2: (p+8) men can complete the work in 10 days less than the number of days required by p men

Options

A. A)Statement (1) alone is sufficient
to answer the question but
statement (2) alone is not sufficient
to answer the question.
B. B)Statement (2) alone is sufficient
to answer the question
but statement (I) alone is not sufficient
to answer the question.
C. C)Both the statements taken together
are necessary to answer
the question, but neither
of the statements alone is sufficient
to answer the question.
D. D)Either Statement (1) or (2) is sufficient.

Answer

To solve the problem, we need to determine the value of \( p \) given the information from the two statements. Let's break it down step by step.

### Given:
- \( p \) men can complete a piece of work in 60 days.

### To Find:
- The value of \( p \).

### Statement 1:
- 30 men can complete the same work in 80 days.

**Step 1: Calculate the total work using Statement 1.**
The total work can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]
From Statement 1:
\[ \text{Total Work} = 30 \text{ men} \times 80 \text{ days} = 2400 \text{ man-days} \]

**Step 2: Relate total work to \( p \) men.**
From the original statement, \( p \) men can complete the work in 60 days:
\[ \text{Total Work} = p \text{ men} \times 60 \text{ days} = 60p \text{ man-days} \]

**Step 3: Set the two expressions for total work equal to each other.**
\[ 60p = 2400 \]

**Step 4: Solve for \( p \).**
\[ p = \frac{2400}{60} = 40 \]

### Conclusion from Statement 1:
Statement 1 alone is sufficient to determine that \( p = 40 \).

---

### Statement 2:
- \( (p + 8) \) men can complete the work in 10 days less than the number of days required by \( p \) men.

**Step 1: Determine the number of days for \( (p + 8) \) men.**
Since \( p \) men take 60 days, \( (p + 8) \) men take:
\[ 60 - 10 = 50 \text{ days} \]

**Step 2: Calculate the total work using Statement 2.**
Using \( (p + 8) \) men:
\[ \text{Total Work} = (p + 8) \text{ men} \times 50 \text{ days} \]
This can be expressed as:
\[ \text{Total Work} = 50(p + 8) \text{ man-days} \]

**Step 3: Set this equal to the work done by \( p \) men.**
From the original statement:
\[ 60p = 50(p + 8) \]

**Step 4: Expand and solve for \( p \).**
\[ 60p = 50p + 400 \]
\[ 60p - 50p = 400 \]
\[ 10p = 400 \]
\[ p = \frac{400}{10} = 40 \]

### Conclusion from Statement 2:
Statement 2 alone is also sufficient to determine that \( p = 40 \).

---

### Final Conclusion:
Both statements independently provide sufficient information to determine the value of \( p \). Thus, the answer is that either statement alone is sufficient.