50 men can dig 40 holes in 30 days. How long will 25 men take to dig 30 holes?

Options

A. 15 days
B. `221//2` days
C. 30 days
D. 45 days

Explanation

To solve the problem step by step, we can use the concept of work done, which is based on the number of men, the number of holes, and the number of days.

### Step 1: Calculate the total work done in man-days
First, we need to determine the total work done in man-days when 50 men dig 40 holes in 30 days.

Total work (in man-days) = Number of men × Number of days
= 50 men × 30 days
= 1500 man-days

### Step 2: Calculate the work done per hole
Now, we can find out how many man-days are required to dig one hole.

Total work for 40 holes = 1500 man-days
Work per hole = Total work / Number of holes
= 1500 man-days / 40 holes
= 37.5 man-days per hole

### Step 3: Calculate the total work needed for 30 holes
Next, we need to calculate the total work required to dig 30 holes.

Total work for 30 holes = Work per hole × Number of holes
= 37.5 man-days per hole × 30 holes
= 1125 man-days

### Step 4: Calculate the number of days required for 25 men to dig 30 holes
Now, we can find out how many days it will take for 25 men to complete the work of digging 30 holes.

Total work = Number of men × Number of days
Rearranging gives us:
Number of days = Total work / Number of men
= 1125 man-days / 25 men
= 45 days

### Final Answer
Thus, it will take 25 men a total of **45 days** to dig 30 holes.

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