On working 10 hourse a day, 15 men can complete a piece of work in 20 days. In how many days can 30 men complete if they work 5 hours per day?

Answer

To solve the problem step by step, we will use the concept of work done, which can be expressed as:

\[ \text{Work} = \text{Men} \times \text{Days} \times \text{Hours per day} \]

### Step 1: Calculate the total work done in the first scenario.
In the first scenario, we have:
- Number of men (M1) = 15
- Number of days (D1) = 20
- Hours worked per day (H1) = 10

Using the formula for work, we can calculate the total work (W):

\[ W = M1 \times D1 \times H1 = 15 \times 20 \times 10 \]

Calculating this:

\[ W = 15 \times 20 = 300 \]
\[ W = 300 \times 10 = 3000 \text{ man-hours} \]

### Step 2: Set up the equation for the second scenario.
In the second scenario, we have:
- Number of men (M2) = 30
- Number of days (D2) = ? (this is what we need to find)
- Hours worked per day (H2) = 5

Using the same work formula, we have:

\[ W = M2 \times D2 \times H2 \]

Substituting the known values:

\[ 3000 = 30 \times D2 \times 5 \]

### Step 3: Solve for D2.
Now we can simplify the equation:

\[ 3000 = 30 \times 5 \times D2 \]
\[ 3000 = 150 \times D2 \]

To find D2, we divide both sides by 150:

\[ D2 = \frac{3000}{150} \]

Calculating this gives:

\[ D2 = 20 \]

### Conclusion:
Thus, 30 men can complete the work in **20 days** if they work 5 hours per day.

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