Working 8 hours a day, 120, persons can dig a canal 162 m long 12 m wide and 2 m deep in 8days . Working 6 hours a day, the number of persons that will be required to dig a canal 729 m long, 10 m wide and 3 m deep in 32 days is

Options

A. 250
B. 175
C. 200
D. 225

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the volume of the first canal
The volume of a canal can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Depth} \]

For the first canal:
- Length = 162 m
- Width = 12 m
- Depth = 2 m

So, the volume is:
\[ \text{Volume} = 162 \times 12 \times 2 \]

### Step 2: Calculate the total work done in person-hours for the first canal
The total work done can be calculated as:
\[ \text{Total Work} = \text{Number of Persons} \times \text{Hours per Day} \times \text{Days} \]

For the first canal:
- Number of Persons = 120
- Hours per Day = 8
- Days = 8

So, the total work done is:
\[ \text{Total Work} = 120 \times 8 \times 8 \]

### Step 3: Calculate the work done per cubic meter for the first canal
Now, we can find the work done per cubic meter by dividing the total work by the volume calculated in Step 1.

### Step 4: Calculate the volume of the second canal
Using the same volume formula for the second canal:
- Length = 729 m
- Width = 10 m
- Depth = 3 m

So, the volume is:
\[ \text{Volume} = 729 \times 10 \times 3 \]

### Step 5: Calculate the total work required for the second canal
Using the work done per cubic meter from Step 3, we can find the total work required for the second canal by multiplying the volume calculated in Step 4 by the work done per cubic meter.

### Step 6: Calculate the number of persons required for the second canal
Using the total work required for the second canal and the working hours per day, we can find the number of persons required:
\[ \text{Number of Persons} = \frac{\text{Total Work Required}}{\text{Hours per Day} \times \text{Days}} \]

For the second canal:
- Hours per Day = 6
- Days = 32

### Final Calculation
Now we can substitute all the values and calculate the number of persons required.