Question

A certain number of men can do a work in 60 days. If there were 8 men more, it could be finished in 10 days less. How many men are there?

• A. 27
• B. 35
• C. 45
• D. 40

Hint:

$60M = 50(M + 8) \implies 10M = 400 \implies M = 40$ men.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Total work is constant and equals the product of the number of men and days ($M_1 D_1 = M_2 D_2$).

Step 2: Key Formula or Approach:
Let the original number of men be $M$.
- $M_1 = M$, $D_1 = 60\,\text{days}$.
- With 8 more men: $M_2 = M + 8$, $D_2 = 60 - 10 = 50\,\text{days}$.
Setting work equations equal:
\[M \times 60 = (M + 8) \times 50\]

Step 3: Detailed Explanation:
Expanding and solving for $M$:
\[60M = 50M + 400 \implies 10M = 400 \implies M = 40\]

Step 4: Final Answer:
Hence, there are 40 men originally.