Three men can complete a piece of work in 18 days. 6 boys can also complete the same piece of work in 18 days. In how many days will 4 men and 4 boys together complete the same piece of work?

Options

A. 10 days
B. 6 days
C. 12 days
D. 9 days

Answer

To solve the problem, we need to determine how many days 4 men and 4 boys will take to complete the same piece of work. We start by calculating the work done by men and boys.

### Step 1: Calculate the work done by men
Given that 3 men can complete the work in 18 days, we can find the total work in terms of man-days.

Total work = Number of men × Number of days
Total work = 3 men × 18 days = 54 man-days

### Step 2: Calculate the work done by boys
Similarly, for the boys, we know that 6 boys can complete the same work in 18 days.

Total work = Number of boys × Number of days
Total work = 6 boys × 18 days = 108 boy-days

### Step 3: Determine the work done by one man and one boy
From the calculations above, we can see that:
- 3 men complete 54 man-days of work.
- 6 boys complete 108 boy-days of work.

To find the efficiency of one man in terms of boys, we can set up the relationship:
1 man = 2 boys (since 3 men = 6 boys)

### Step 4: Calculate the combined work rate of 4 men and 4 boys
Now, we need to find the work done by 4 men and 4 boys together.

- Work done by 4 men:
4 men = 4 × 1 = 4 man units of work

- Work done by 4 boys:
4 boys = 4 × (1/2) = 2 man units of work (since 1 boy = 1/2 man)

### Step 5: Total work done by 4 men and 4 boys
Total work done by 4 men and 4 boys together:
Total work = Work done by men + Work done by boys
Total work = 4 man units + 2 man units = 6 man units of work per day

### Step 6: Calculate the number of days to complete the work
Now, we know the total work is 54 man-days and the combined work rate of 4 men and 4 boys is 6 man units per day.

To find the number of days required to complete the work:
Number of days = Total work / Work done per day
Number of days = 54 man-days / 6 man units per day = 9 days

Thus, 4 men and 4 boys together will complete the work in **9 days**.

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