If 10 boys walk 10 km in 10 days, then how many days it will take for 3 boys to walk 10 km?

Options

A. a)33.33
B. b)36
C. c)66.66
D. d)10

Explanation

To solve the problem step by step, we can use the concept of work done, which can be expressed in terms of the number of boys, the number of days, and the distance walked.

### Step 1: Understand the given information
We know that:
- 10 boys can walk 10 km in 10 days.

### Step 2: Calculate the total work done
The total work done can be represented as:
\[ \text{Work} = \text{Number of Boys} \times \text{Number of Days} \]
So, for the first scenario:
\[ \text{Work} = 10 \text{ boys} \times 10 \text{ days} = 100 \text{ boy-days} \]

### Step 3: Set up the equation for the second scenario
Now, we need to find out how many days it will take for 3 boys to walk the same distance of 10 km. Let \( D_2 \) be the number of days it takes for 3 boys to walk 10 km. The work done in this scenario can be expressed as:
\[ \text{Work} = 3 \text{ boys} \times D_2 \text{ days} \]

### Step 4: Equate the work done in both scenarios
Since the work done in both scenarios is the same (10 km), we can set the equations equal to each other:
\[ 100 \text{ boy-days} = 3 \text{ boys} \times D_2 \text{ days} \]

### Step 5: Solve for \( D_2 \)
Now, we can solve for \( D_2 \):
\[ D_2 = \frac{100 \text{ boy-days}}{3 \text{ boys}} \]
\[ D_2 = \frac{100}{3} \]
\[ D_2 \approx 33.33 \text{ days} \]

### Conclusion
It will take approximately 33.33 days for 3 boys to walk 10 km.