Question

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

• A. 10
• B. 12
• C. 13
• D. 14

Answer 1

The Correct Option is C

Assume one machine completes 1 unit of work per day.

Given that two machines together complete the job in 13 days, the total work is:

\[ \text{Work} = 2 \times 1 \times 13 = 26 \text{ units} \]

Let the daily work output of one man be denoted by \( m \).

We are told: \[ 3m + 8 \times 1 = 2(8m + 3 \times 1) \]

Solving: \[ 3m + 8 = 16m + 6 \Rightarrow 3m - 16m = 6 - 8 \Rightarrow -13m = -2 \Rightarrow m = \frac{2}{13} \]

Now, let \( x \) be the number of men required to complete 26 units of work in 13 days. Then, using the formula:

\[ x \cdot m \cdot 13 = 26 \Rightarrow x \cdot \frac{2}{13} \cdot 13 = 26 \Rightarrow x \cdot 2 = 26 \Rightarrow x = 13 \]

Final Answer:

\[ \boxed{13 \text{ men}} \]