30 girls can finish a work in 40 days. After how many days should 10 girls leave the work so that it may be finished in 46 days, if all the 30 girls started the work?

Options

A. 18 days
B. 28 days
C. 22 days
D. 30 days

Answer

To solve the problem, we need to determine after how many days 10 girls should leave the work so that the remaining work can be completed in a total of 46 days.

### Step-by-Step Solution:

1. **Calculate the Total Work**:
The total work can be calculated in terms of "girl-days". If 30 girls can finish the work in 40 days, the total work is:
\[ \text{Total Work} = 30 \text{ girls} \times 40 \text{ days} = 1200 \text{ girl-days} \]

**Hint**: Remember that "girl-days" is a way to express the total amount of work done by a certain number of girls over a certain number of days.

2. **Determine the Work Done in 46 Days**:
Since we want the work to be completed in 46 days, we need to find out how much work can be done by 30 girls in the initial days and then by 20 girls after 10 girls leave.

3. **Let x be the number of days all 30 girls work**:
In the first x days, the work done by 30 girls is:
\[ \text{Work done} = 30 \text{ girls} \times x \text{ days} = 30x \text{ girl-days} \]

4. **Calculate Remaining Days**:
After x days, the remaining days to complete the work will be:
\[ \text{Remaining Days} = 46 - x \]

5. **Work Done by Remaining Girls**:
After x days, 10 girls leave, so 20 girls will work for the remaining days. The work done by 20 girls in the remaining days is:
\[ \text{Work done} = 20 \text{ girls} \times (46 - x) \text{ days} = 20(46 - x) \text{ girl-days} \]

6. **Set Up the Equation**:
The total work done by both phases must equal the total work:
\[ 30x + 20(46 - x) = 1200 \]

7. **Simplify the Equation**:
Expanding the equation gives:
\[ 30x + 920 - 20x = 1200 \]
\[ 10x + 920 = 1200 \]

8. **Solve for x**:
Subtract 920 from both sides:
\[ 10x = 280 \]
Divide by 10:
\[ x = 28 \]

9. **Conclusion**:
Therefore, the 10 girls should leave after 28 days.

### Final Answer:
10 girls should leave the work after **28 days**.