Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of the work in

Options

A. 9 days
B. 6 days
C. 5 days
D. 3 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know that a certain number of persons can complete a piece of work in 12 days. Let's denote the number of persons as \( P \).

### Step 2: Calculate the total work
The total work can be represented as:
\[ \text{Total Work} = P \times 12 \text{ days} \]
This means that \( P \) persons can complete \( P \times 12 \) units of work in 12 days.

### Step 3: Determine the new number of persons
According to the problem, two times the number of persons will be working. Therefore, the new number of persons is:
\[ 2P \]

### Step 4: Calculate the amount of work done by the new group
The new group of \( 2P \) persons will be doing work. Since they are twice as many, they will complete the same total work in less time.

### Step 5: Calculate the time taken to complete half the work
We need to find out how long it will take for \( 2P \) persons to complete half of the total work. Half of the total work is:
\[ \text{Half Work} = \frac{P \times 12}{2} = 6P \]

### Step 6: Calculate the time taken by \( 2P \) persons to complete half the work
The rate of work done by \( 2P \) persons is:
\[ \text{Work Rate} = 2P \text{ persons} \times \text{Days} \]
To find the time taken (let's denote it as \( T \)), we can set up the equation:
\[ 2P \times T = 6P \]

### Step 7: Solve for \( T \)
Dividing both sides by \( 2P \) (assuming \( P \neq 0 \)):
\[ T = \frac{6P}{2P} = 3 \text{ days} \]

### Conclusion
Thus, two times the number of such persons will do half of the work in **3 days**.

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