Working 7 hours a day, 18 persons can complete a certain work in 32 days. In how many days would 14 persons complete the same work, working 8 hours a day ?

Options

A. 42
B. 30
C. 35
D. 36

Answer

To solve the problem step by step, we can use the formula for total work, which is given by:

\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} \times \text{Number of Hours per Day} \]

### Step 1: Calculate the total work done by 18 persons in 32 days working 7 hours a day.

Using the formula:
- Number of Persons (P) = 18
- Number of Days (D) = 32
- Number of Hours per Day (H) = 7

Total Work (W) can be calculated as:
\[ W = P \times D \times H \]
\[ W = 18 \times 32 \times 7 \]

### Step 2: Calculate the total work.

Now, let's perform the multiplication:
\[ W = 18 \times 32 = 576 \]
\[ W = 576 \times 7 = 4032 \]

So, the total work is 4032 units.

### Step 3: Set up the equation for 14 persons working 8 hours a day.

Now we need to find out how many days (let's call it D') it will take for 14 persons working 8 hours a day to complete the same amount of work (4032 units).

Using the same formula:
- Number of Persons (P') = 14
- Number of Hours per Day (H') = 8
- Number of Days (D') = ?

We can set up the equation:
\[ 4032 = P' \times D' \times H' \]
\[ 4032 = 14 \times D' \times 8 \]

### Step 4: Solve for D'.

Now we can solve for D':
\[ 4032 = 14 \times D' \times 8 \]
\[ 4032 = 112 \times D' \]

Now, divide both sides by 112:
\[ D' = \frac{4032}{112} \]

### Step 5: Calculate D'.

Now, let's perform the division:
\[ D' = 36 \]

### Conclusion

So, it would take 14 persons working 8 hours a day a total of **36 days** to complete the same work.