It is given that 16men working 18hr per day can build a wall 36m long, 4m broad and 24m high in 20 days . How many men will be required to build a wall 64 m long 6m broad and 18m high working 12hr per day in 16 days ?

Options

A. 60
B. 20
C. 30
D. 35

Answer

To solve the problem step by step, we will use the concept of work done, which can be calculated as the product of the number of men, the number of hours they work per day, and the number of days they work.

### Step 1: Calculate the total work done in the first case
The total work done can be calculated using the formula:
\[ \text{Work} = \text{Length} \times \text{Breadth} \times \text{Height} \]

For the first wall:
- Length = 36 m
- Breadth = 4 m
- Height = 24 m

So, the total work done (W1) is:
\[ W_1 = 36 \times 4 \times 24 \]

### Step 2: Calculate the total work done in the first case
Now, let's calculate \( W_1 \):
\[ W_1 = 36 \times 4 \times 24 = 3456 \, \text{m}^3 \]

### Step 3: Calculate the total man-hours in the first case
The total man-hours can be calculated as:
\[ \text{Total Man-Hours} = \text{Number of Men} \times \text{Hours per Day} \times \text{Days} \]

For the first case:
- Number of Men (M1) = 16
- Hours per Day (D1) = 18
- Days (T1) = 20

So, the total man-hours (M1) is:
\[ M_1 = 16 \times 18 \times 20 \]

### Step 4: Calculate the total man-hours in the first case
Now, let's calculate \( M_1 \):
\[ M_1 = 16 \times 18 \times 20 = 5760 \, \text{man-hours} \]

### Step 5: Calculate the work done per man-hour
Now, we can find the work done per man-hour in the first case:
\[ \text{Work per Man-Hour} = \frac{W_1}{M_1} = \frac{3456}{5760} \]

### Step 6: Calculate the work done per man-hour
Now, let's calculate:
\[ \text{Work per Man-Hour} = \frac{3456}{5760} = 0.6 \, \text{m}^3/\text{man-hour} \]

### Step 7: Calculate the total work required for the second wall
For the second wall:
- Length = 64 m
- Breadth = 6 m
- Height = 18 m

So, the total work required (W2) is:
\[ W_2 = 64 \times 6 \times 18 \]

### Step 8: Calculate the total work required for the second wall
Now, let's calculate \( W_2 \):
\[ W_2 = 64 \times 6 \times 18 = 6912 \, \text{m}^3 \]

### Step 9: Calculate the total man-hours available in the second case
For the second case:
- Hours per Day (D2) = 12
- Days (T2) = 16

Now, we need to find the total man-hours (M2):
\[ M_2 = \text{Number of Men} \times 12 \times 16 \]

### Step 10: Set up the equation to find the number of men required
Let the number of men required be \( x \). Then:
\[ x \times 12 \times 16 = \text{Total Work Required} \]

### Step 11: Substitute the values and solve for x
Using the work done per man-hour:
\[ x \times 12 \times 16 = 6912 \]
\[ x \times 192 = 6912 \]
\[ x = \frac{6912}{192} \]

### Step 12: Calculate the number of men required
Now, let's calculate:
\[ x = 36 \]

### Final Answer
The number of men required to build the second wall is **36 men**.