If 14 men and 12 boys can finish work in 4 days , while 8 men and 16 boys can finish the same work in 5 days . Compare the 1 day work of 1 man and 1 boy .

Options

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

Answer

To solve the problem, we need to find the work done by one man and one boy based on the information provided. Let's break it down step by step.

### Step 1: Understand the given information
We have two scenarios:
1. 14 men and 12 boys can finish the work in 4 days.
2. 8 men and 16 boys can finish the same work in 5 days.

### Step 2: Set up the equations
Let the work done by one man in one day be \( M \) and the work done by one boy in one day be \( B \).

From the first scenario:
- Total work done by 14 men and 12 boys in 4 days:
\[ \text{Total Work} = (14M + 12B) \times 4 \]

From the second scenario:
- Total work done by 8 men and 16 boys in 5 days:
\[ \text{Total Work} = (8M + 16B) \times 5 \]

Since both expressions represent the same total work, we can set them equal to each other:
\[ (14M + 12B) \times 4 = (8M + 16B) \times 5 \]

### Step 3: Simplify the equation
Expanding both sides:
\[ 56M + 48B = 40M + 80B \]

### Step 4: Rearranging the equation
Now, we can rearrange the equation to isolate terms involving \( M \) and \( B \):
\[ 56M - 40M = 80B - 48B \]
\[ 16M = 32B \]

### Step 5: Find the ratio of work done
Dividing both sides by 16:
\[ M = 2B \]

This means the work done by one man in one day is twice the work done by one boy in one day.

### Step 6: Conclusion
The comparison of the one day work of one man and one boy is:
\[ \text{Work done by 1 man} : \text{Work done by 1 boy} = 2 : 1 \]