12 men can make 80 tables in 20 days working 8 hours a day. In how many days 30 men can make 120 tables working 6 hours a day?
(a)16
(b)23
(c)13
(D)15

Answer

To solve the problem, we will use the relationship between men, days, hours, and work. The formula we will use is:

\[ \text{Work} = \text{Men} \times \text{Days} \times \text{Hours} \]

### Step 1: Calculate the total work done in the first scenario
We know that:
- 12 men can make 80 tables in 20 days working 8 hours a day.

Using the formula:
\[ \text{Work} = \text{Men} \times \text{Days} \times \text{Hours} \]
\[ \text{Work} = 12 \times 20 \times 8 \]

Calculating this:
\[ \text{Work} = 12 \times 20 = 240 \]
\[ \text{Work} = 240 \times 8 = 1920 \text{ man-hours} \]

This means that the total work required to make 80 tables is 1920 man-hours.

### Step 2: Determine the work required for the second scenario
Now we need to find out how many days it will take for 30 men to make 120 tables working 6 hours a day.

### Step 3: Calculate the work for 120 tables
Since we know that 80 tables require 1920 man-hours, we can find the work required for 120 tables using a proportion:
\[ \text{Work for 120 tables} = \frac{120}{80} \times 1920 \]
\[ \text{Work for 120 tables} = 1.5 \times 1920 = 2880 \text{ man-hours} \]

### Step 4: Set up the equation for the second scenario
Now we set up the equation for the second scenario where we have:
- 30 men working
- 6 hours a day
- Let \( D \) be the number of days required.

Using the work formula:
\[ \text{Work} = \text{Men} \times \text{Days} \times \text{Hours} \]
\[ 2880 = 30 \times D \times 6 \]

### Step 5: Solve for \( D \)
Now we can solve for \( D \):
\[ 2880 = 180D \]
\[ D = \frac{2880}{180} \]
\[ D = 16 \]

Thus, it will take 30 men 16 days to make 120 tables working 6 hours a day.

### Final Answer:
The answer is (a) 16.