40 persons can repair a bridge in 12 days. If 8 more persons join them, then in how many days bridge can be repaired?

Options

A. a) 11 days
B. b) 10 days
C. c) 9 days
D. d) 8 days

Answer

To solve the problem step by step, we can use the concept of work done, which is calculated using the formula:

\[ \text{Work} = \text{Number of Persons} \times \text{Days} \times \text{Hours} \]

In this case, we'll assume that the work done in one day is 1 hour for simplicity.

### Step 1: Calculate the total work done by the initial group of workers.

Given:
- Number of persons (m1) = 40
- Days (d1) = 12

Using the formula for work, we have:

\[ \text{Total Work} (w1) = m1 \times d1 = 40 \times 12 = 480 \text{ person-days} \]

### Step 2: Determine the new number of workers.

If 8 more persons join the initial group of 40, the new number of persons (m2) will be:

\[ m2 = 40 + 8 = 48 \]

### Step 3: Set up the equation for the new scenario.

Let \(d2\) be the number of days required to complete the same amount of work with the new number of workers. The total work remains the same:

\[ \text{Total Work} (w2) = m2 \times d2 = 48 \times d2 \]

### Step 4: Equate the total work from both scenarios.

Since the total work is the same in both cases:

\[ 480 = 48 \times d2 \]

### Step 5: Solve for \(d2\).

To find \(d2\), rearrange the equation:

\[ d2 = \frac{480}{48} = 10 \]

### Conclusion

The bridge can be repaired in **10 days** with the additional workers.

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