20 workers working for 5 h per day complete a work in 10 days. If 25 workers are employed to work 10 h per day, what is the time required to complete the work?

Options

A. 4 days
B. 5 days
C. 6 days
D. 8 days

Answer

To solve the problem step by step, we will use the concept of work done, which can be calculated using the formula:

\[ \text{Work} = \text{Number of Workers} \times \text{Time} \times \text{Hours Worked per Day} \]

### Step 1: Calculate the total work done by the first group of workers.

Given:
- Number of workers (M1) = 20
- Time (D1) = 10 days
- Hours worked per day (T1) = 5 hours

Using the formula:
\[ \text{Total Work} = M1 \times D1 \times T1 \]
\[ \text{Total Work} = 20 \times 10 \times 5 = 1000 \text{ worker-hours} \]

### Step 2: Set up the equation for the second group of workers.

Now, we need to find out how many days (D2) it will take for the second group of workers to complete the same amount of work.

Given for the second group:
- Number of workers (M2) = 25
- Hours worked per day (T2) = 10 hours
- Days (D2) = ?

Using the same work formula:
\[ \text{Total Work} = M2 \times D2 \times T2 \]
Since the total work remains the same, we can set up the equation:
\[ 1000 = 25 \times D2 \times 10 \]

### Step 3: Solve for D2.

Rearranging the equation to solve for D2:
\[ 1000 = 250 \times D2 \]
\[ D2 = \frac{1000}{250} = 4 \]

### Conclusion

The time required to complete the work with 25 workers working 10 hours per day is **4 days**.

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