3 men or 15 boys can do a piece of work in 30 days. In how many days…

The correct answer is Option (3) → 30 days

1. Find the efficiency ratio:

The problem states that 3 men do the same work as 15 boys.

$3 \text{ Men} = 15 \text{ Boys}$

$1 \text{ Man} = 5 \text{ Boys}$

2. Calculate the Total Work:

Total work can be defined as the number of workers multiplied by the days taken. Let’s use the boys to define the work:

$\text{Total Work} = 15 \text{ Boys} \times 30 \text{ Days} = \mathbf{450 \text{ boy-days}}$

3. Convert the new group into a single unit:

We need to find how long it takes for 2 men and 5 boys to finish. Let's convert the men into boys using the ratio found in Step 1 ($1 \text{ Man} = 5 \text{ Boys}$):

$\text{New Group} = 2 \text{ Men} + 5 \text{ Boys}$

$\text{New Group} = 2(5 \text{ Boys}) + 5 \text{ Boys}$

$\text{New Group} = 10 \text{ Boys} + 5 \text{ Boys} = \mathbf{15 \text{ Boys}}$

4. Find the Number of Days:

$\text{Days} = \frac{\text{Total Work}}{\text{New Group Strength}}$

$\text{Days} = \frac{450 \text{ boy-days}}{15 \text{ boys}} = \mathbf{30 \text{ days}}$