Question

A certain number of men can complete a piece of work in 60 days. If there were 8 more men, the work could be finished in 10 days less. How many men were there originally?

• A. 40
• B. 50
• C. 80
• D. 100
• E. 110

Answer 1

The Correct Option is A

Step 1: Understand the problem.
Let the number of men originally be \( x \). They can complete the work in 60 days. If there were 8 more men, the work would be completed in 10 days less, i.e., in 50 days. We need to find the value of \( x \).

Step 2: Use the formula for work.
The total work can be expressed as the product of the number of men and the number of days taken to complete the work.
- The total work done by \( x \) men in 60 days is \( x \times 60 \). - The total work done by \( x + 8 \) men in 50 days is \( (x + 8) \times 50 \).

Since the total work is the same in both cases, we can set the two expressions for the total work equal to each other:
\( x \times 60 = (x + 8) \times 50 \)

Step 3: Solve the equation.
Expanding both sides of the equation:
\( 60x = 50(x + 8) \)
\( 60x = 50x + 400 \)
\( 60x - 50x = 400 \)
\( 10x = 400 \)
\( x = \frac{400}{10} \)
\( x = 40 \)

Step 4: Conclusion.
The number of men originally was 40.

Final Answer:
The correct option is (A): 40.