Thirty persons working 6 hours a day can complete a work in 28 days. How many days will 28 persons take to complete another work which is two times the present work, if they work 9 hours a day?

Options

A. a) 36
B. b) 45
C. c) 42
D. d) 40

Answer

To solve the problem step by step, we will use the concept of the MDH (Men-Days-Hours) formula.

### Step 1: Calculate the total work done in terms of man-hours
Given:
- Number of persons (M1) = 30
- Hours worked per day (H1) = 6
- Days worked (D1) = 28

Total work (W1) can be calculated as:
\[ W1 = M1 \times D1 \times H1 \]
Substituting the values:
\[ W1 = 30 \times 28 \times 6 \]

### Step 2: Calculate the total work
Now, calculate the total work:
\[ W1 = 30 \times 28 \times 6 = 5040 \text{ man-hours} \]

### Step 3: Determine the work for the second scenario
The second work (W2) is two times the first work:
\[ W2 = 2 \times W1 = 2 \times 5040 = 10080 \text{ man-hours} \]

### Step 4: Set up the equation for the second scenario
Now we have:
- Number of persons (M2) = 28
- Hours worked per day (H2) = 9
- Days worked (D2) = ? (this is what we need to find)

Using the MDH formula:
\[ M1 \times D1 \times H1 = M2 \times D2 \times H2 \]
Substituting the known values:
\[ 30 \times 28 \times 6 = 28 \times D2 \times 9 \]

### Step 5: Simplify the equation
Now we can simplify:
\[ 5040 = 28 \times D2 \times 9 \]
\[ 5040 = 252 \times D2 \]

### Step 6: Solve for D2
To find D2, divide both sides by 252:
\[ D2 = \frac{5040}{252} \]
Calculating this gives:
\[ D2 = 20 \]

### Step 7: Calculate the final answer
Since we need to account for the fact that the work is double, we should multiply D2 by 2:
\[ D2 = 20 \text{ days} \]

### Conclusion
Thus, it will take 40 days for 28 persons to complete the work which is two times the present work if they work 9 hours a day.