If the work done by 8 men and 4 boys in 1 day is 7 times the work done by 1 man and 1 boy, then compare the work done by 1 man and 1 boy in 1 day?

Options

A. 1
B. 2
C. 3
D. `1/2`

Answer

To solve the problem step-by-step, let's denote:

- The work done by 1 man in one day as \( M \).
- The work done by 1 boy in one day as \( B \).

According to the problem, we have the following information:

1. The work done by 8 men and 4 boys in one day is given by:
\[ \text{Work by 8 men and 4 boys} = 8M + 4B \]

2. The work done by 1 man and 1 boy in one day is given by:
\[ \text{Work by 1 man and 1 boy} = M + B \]

3. It is stated that the work done by 8 men and 4 boys in one day is 7 times the work done by 1 man and 1 boy:
\[ 8M + 4B = 7(M + B) \]

### Step 1: Set up the equation
From the above relation, we can set up the equation:
\[ 8M + 4B = 7M + 7B \]

### Step 2: Rearrange the equation
Now, rearranging the equation to isolate terms involving \( M \) and \( B \):
\[ 8M - 7M + 4B - 7B = 0 \]
This simplifies to:
\[ M - 3B = 0 \]

### Step 3: Solve for the relationship between M and B
From the equation \( M - 3B = 0 \), we can express \( M \) in terms of \( B \):
\[ M = 3B \]

### Step 4: Compare the work done by 1 man and 1 boy
Now, we can find the work done by 1 man and 1 boy:
\[ M + B = 3B + B = 4B \]

### Conclusion
Thus, the work done by 1 man and 1 boy in one day is \( 4B \), which shows that the work done by 1 man is 3 times the work done by 1 boy.