30 workers can finish a work in 20 days. After how many days should 9 workers leave the job so that the work is completed in total 26 days if all the 30 workers started the work.

Options

A. 12
B. 10
C. 6
D. none of these

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Problem
We know that 30 workers can complete a job in 20 days. We need to find out after how many days 9 workers should leave the job so that the total work is completed in 26 days.

### Step 2: Calculate Total Work
First, we calculate the total amount of work in terms of worker-days.
- Total work (W) = Number of workers × Number of days = 30 workers × 20 days = 600 worker-days.

### Step 3: Define Variables
Let \( X \) be the number of days after which 9 workers leave the job. This means that for the first \( X \) days, all 30 workers are working.

### Step 4: Calculate Work Done in First X Days
The work done by 30 workers in \( X \) days is:
- Work done = Number of workers × Number of days = 30 workers × \( X \) days = \( 30X \) worker-days.

### Step 5: Calculate Remaining Work
The total work is 600 worker-days. The remaining work after \( X \) days is:
- Remaining work = Total work - Work done in first \( X \) days = \( 600 - 30X \).

### Step 6: Determine Remaining Days
After \( X \) days, the total time to complete the work is 26 days. Therefore, the remaining days after \( X \) days is:
- Remaining days = Total days - Days worked = \( 26 - X \).

### Step 7: Calculate Work Done by Remaining Workers
After \( X \) days, 21 workers (30 - 9) will continue the work for \( 26 - X \) days. The work done by these 21 workers is:
- Work done = Number of workers × Number of days = 21 workers × \( (26 - X) \) days = \( 21(26 - X) \) worker-days.

### Step 8: Set Up the Equation
The total work done must equal the total work required:
\[ 30X + 21(26 - X) = 600. \]

### Step 9: Solve the Equation
Expanding the equation:
\[ 30X + 546 - 21X = 600. \]
Combine like terms:
\[ 9X + 546 = 600. \]
Subtract 546 from both sides:
\[ 9X = 54. \]
Divide by 9:
\[ X = 6. \]

### Conclusion
Thus, 9 workers should leave the job after 6 days.