15 persons can complete a work in 60 days. If the number of persons is increased by 5, how many days earlier will the work get completed ?

Options

A. 5 days
B. 10 days
C. 15 days
D. 45 days

Answer

To solve the problem, we need to determine how many days earlier the work will be completed when the number of workers is increased from 15 to 20. Here’s a step-by-step solution:

### Step 1: Calculate the total work in person-days
First, we calculate the total amount of work done in person-days. If 15 persons can complete the work in 60 days, the total work can be calculated as:
\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} = 15 \times 60 = 900 \text{ person-days} \]

**Hint:** To find the total work, multiply the number of workers by the number of days they work.

### Step 2: Determine the new number of workers
Next, we increase the number of workers by 5. Therefore, the new number of workers is:
\[ \text{New Number of Persons} = 15 + 5 = 20 \]

**Hint:** When the number of workers increases, simply add the increase to the original number of workers.

### Step 3: Calculate the number of days required with the new number of workers
Now, we need to find out how many days it will take for 20 persons to complete the same amount of work (900 person-days). We can set up the equation:
\[ \text{Number of Days} = \frac{\text{Total Work}}{\text{Number of Persons}} = \frac{900}{20} \]
Calculating this gives:
\[ \text{Number of Days} = 45 \text{ days} \]

**Hint:** To find the number of days required, divide the total work by the new number of workers.

### Step 4: Calculate how many days earlier the work gets completed
Now, we find out how many days earlier the work is completed by subtracting the new number of days from the original number of days:
\[ \text{Days Earlier} = \text{Original Days} - \text{New Days} = 60 - 45 = 15 \text{ days} \]

**Hint:** To find out how much earlier the work is completed, subtract the new completion time from the original completion time.

### Final Answer
The work will be completed **15 days earlier**.