Fifteen men take 30 days to complete a piece of work, working 8 hours a day. Find the time taken by 30 men to complete 5 times as much work, working 10 hours a day.

Options

A. 30 days
B. 45 days
C. 60 days
D. 15 days

Explanation

To solve the problem step by step, we will use the concept of work, which can be expressed in terms of the number of men, the number of days they work, and the number of hours they work each day.

### Step 1: Calculate the total work done by the first group of men.
The total work (W) can be calculated using the formula:
\[ W = \text{Number of Men} \times \text{Number of Days} \times \text{Hours per Day} \]
For the first group:
- Number of Men (m1) = 15
- Number of Days (d1) = 30
- Hours per Day (h1) = 8

So, the total work done (W1) is:
\[ W1 = 15 \times 30 \times 8 \]
Calculating this gives:
\[ W1 = 3600 \text{ man-hours} \]

### Step 2: Determine the total work for the second group.
The second group is tasked with completing 5 times the original work:
\[ W2 = 5 \times W1 = 5 \times 3600 = 18000 \text{ man-hours} \]

### Step 3: Set up the equation for the second group of men.
Now, we need to find out how many days (d2) it will take for 30 men (m2) working 10 hours a day (h2) to complete this work:
- Number of Men (m2) = 30
- Hours per Day (h2) = 10

We use the work formula again:
\[ W2 = m2 \times d2 \times h2 \]
Substituting the known values:
\[ 18000 = 30 \times d2 \times 10 \]

### Step 4: Solve for d2.
Now, we simplify the equation:
\[ 18000 = 300 \times d2 \]
To find d2, divide both sides by 300:
\[ d2 = \frac{18000}{300} \]
Calculating this gives:
\[ d2 = 60 \text{ days} \]

### Final Answer
The time taken by 30 men to complete 5 times as much work, working 10 hours a day, is **60 days**.

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