Two workers undertake to do a job. The second-worker started working 2 hours after the first. Five hours after the second worker has begun working there is still `9/20` work to be done. When the assignment is completed, it turns out that first worker has done `60%` of the work, while second worker has done rest of the work. How many hours would it take each one to do the whole job individually?

Options

A. 10 hours and 12 hours
B. 15 hours and 10 hours
C. 20 hours and 25 hours
D. 18 hours and 20 hours

Answer

To solve the problem step by step, we need to analyze the work done by both workers and the time they took to complete the job.

### Step-by-Step Solution:

1. **Understanding the Work Remaining**:
- The problem states that after the second worker has worked for 5 hours, there is still \( \frac{9}{20} \) of the work left.
- This means that \( 1 - \frac{9}{20} = \frac{11}{20} \) of the work has been completed.

2. **Percentage of Work Done**:
- The completed work \( \frac{11}{20} \) can be converted to percentage:
\[ \frac{11}{20} \times 100 = 55\% \]
- Therefore, 55% of the work has been done.

3. **Distribution of Work**:
- It is given that the first worker completed 60% of the total work, while the second worker completed the remaining 40%.
- Since 55% of the work is done, we can relate this to the contributions of both workers:
- Let \( W_1 \) be the work done by the first worker and \( W_2 \) be the work done by the second worker.
- From the problem, we know:
\[ W_1 + W_2 = 55\% \]
where \( W_1 = 60\% \) of total work and \( W_2 = 40\% \) of total work.

4. **Time Worked by Each Worker**:
- The first worker worked for 7 hours (2 hours before the second worker started and 5 hours while the second worker worked).
- The second worker worked for 5 hours.

5. **Setting Up the Equations**:
- Let the work rates of the first and second workers be \( R_1 \) and \( R_2 \) respectively.
- The total work done can be expressed as:
\[ R_1 \times 7 + R_2 \times 5 = 55\% \]

6. **Using the Work Contribution**:
- Since \( W_1 = 60\% \) and \( W_2 = 40\% \), we can express the work done by each worker in terms of their rates:
\[ R_1 \times 7 = 0.6 \quad \text{(60% of total work)} \]
\[ R_2 \times 5 = 0.4 \quad \text{(40% of total work)} \]

7. **Finding the Rates**:
- From the first equation:
\[ R_1 = \frac{0.6}{7} \quad \text{(work rate of first worker)} \]
- From the second equation:
\[ R_2 = \frac{0.4}{5} \quad \text{(work rate of second worker)} \]

8. **Calculating Individual Work Time**:
- To find how long it would take each worker to complete the whole job individually, we take the reciprocal of their rates:
\[ \text{Time for first worker} = \frac{1}{R_1} = \frac{7}{0.6} = \frac{70}{6} \approx 11.67 \text{ hours} \]
\[ \text{Time for second worker} = \frac{1}{R_2} = \frac{5}{0.4} = \frac{50}{4} = 12.5 \text{ hours} \]

### Final Answer:
- The first worker would take approximately **11.67 hours** to complete the job individually.
- The second worker would take **12.5 hours** to complete the job individually.