20 men can cut 30 trees in 4 h. If 4 men leave the job, how many trees will be cut in 12 h?

Options

A. 72
B. 80
C. 68
D. 79

Answer

To solve the problem step by step, we will use the concept of work done, which can be expressed as:

\[ \text{Work} = \text{Number of Men} \times \text{Time} \times \text{Rate of Work} \]

### Step 1: Determine the Rate of Work
We know that 20 men can cut 30 trees in 4 hours.

First, we find the total work done in terms of "trees per hour":
\[ \text{Total Work} = 30 \text{ trees} \]
\[ \text{Total Time} = 4 \text{ hours} \]
\[ \text{Rate of Work} = \frac{\text{Total Work}}{\text{Total Time}} = \frac{30 \text{ trees}}{4 \text{ hours}} = 7.5 \text{ trees per hour} \]

### Step 2: Calculate Work Done by One Man
Now we need to find out how much work one man can do in one hour. Since 20 men can cut 7.5 trees in one hour:
\[ \text{Work done by one man in one hour} = \frac{7.5 \text{ trees}}{20 \text{ men}} = 0.375 \text{ trees per man per hour} \]

### Step 3: Calculate the Number of Men Remaining
If 4 men leave the job, the number of men left is:
\[ \text{Remaining Men} = 20 - 4 = 16 \text{ men} \]

### Step 4: Calculate the Total Work Done by Remaining Men in 12 Hours
Now we calculate how many trees 16 men can cut in 12 hours:
\[ \text{Total Work by 16 men in 12 hours} = \text{Number of Men} \times \text{Time} \times \text{Work done by one man in one hour} \]
\[ = 16 \text{ men} \times 12 \text{ hours} \times 0.375 \text{ trees per man per hour} \]
\[ = 16 \times 12 \times 0.375 \]

### Step 5: Perform the Calculation
Now we perform the multiplication:
\[ 16 \times 12 = 192 \]
\[ 192 \times 0.375 = 72 \]

### Conclusion
Thus, the total number of trees that will be cut in 12 hours by the remaining 16 men is:
\[ \text{Total Trees Cut} = 72 \text{ trees} \]

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