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 :

Options

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

Answer

To solve the problem, we need to determine how many days 9 workers can work before leaving, such that the total work is completed in 26 days.

### Step-by-Step Solution:

1. **Calculate Total Work in Worker-Days**:
- If 30 workers can finish the work in 20 days, the total work can be calculated as:
\[ \text{Total Work} = \text{Number of Workers} \times \text{Number of Days} = 30 \times 20 = 600 \text{ worker-days} \]

**Hint**: Remember that total work is the product of the number of workers and the time they work.

2. **Determine the Work Done by 30 Workers in 'x' Days**:
- Let 'x' be the number of days that all 30 workers work before 9 workers leave. The work done in 'x' days is:
\[ \text{Work Done} = 30 \times x \]

**Hint**: Use the same formula for work done as in step 1, but adjust the number of days.

3. **Calculate Remaining Days**:
- After 'x' days, there are \(26 - x\) days left to complete the work. During these remaining days, only 21 workers (30 - 9) will be working. The work done in these remaining days is:
\[ \text{Work Done} = 21 \times (26 - x) \]

**Hint**: Remember to subtract the days already worked from the total days to find the remaining days.

4. **Set Up the Equation**:
- The total work done must equal the total work required:
\[ 30x + 21(26 - x) = 600 \]

**Hint**: Combine the work done by both groups of workers into one equation.

5. **Simplify the Equation**:
- Expanding the equation:
\[ 30x + 546 - 21x = 600 \]
- Combine like terms:
\[ 9x + 546 = 600 \]

**Hint**: Make sure to combine all terms carefully to isolate 'x'.

6. **Solve for 'x'**:
- Subtract 546 from both sides:
\[ 9x = 600 - 546 \]
\[ 9x = 54 \]
- Divide by 9:
\[ x = 6 \]

**Hint**: When solving for 'x', remember to perform the same operation on both sides of the equation.

7. **Conclusion**:
- Therefore, 9 workers should leave the job after **6 days**.

### Final Answer:
9 workers should leave the job after **6 days** so that the work is completed in a total of 26 days.