Question

A can complete a job in 12 days and B in 15 days. They work together for 5 days, and then A leaves. How many more days will B take to finish the remaining work?

• A. 3.75
• B. 5
• C. 3
• D. 6

Hint:

Convert individual time to daily work rate using \( \frac{1}{\text{days}} \), and multiply by number of working days to find total work done.

Answer 1

The Correct Option is A

To solve the problem, we need to determine how many days B will take to complete the remaining work after working with A for a few days.

1. Understanding the Concepts:

- Work and Time: If a person can complete a job in 'n' days, their 1 day work is \( \frac{1}{n} \).
- Combined Work: When two people work together, their combined 1 day work is the sum of their individual 1 day work.
- Remaining Work: Subtract the work done from the total work (which is considered as 1 full unit).

2. Given Values:

- A completes the job in 12 days → A’s 1 day work = \( \frac{1}{12} \)
- B completes the job in 15 days → B’s 1 day work = \( \frac{1}{15} \)
- Time working together = 5 days

3. Calculating the Work Done Together:

Combined 1 day work = \( \frac{1}{12} + \frac{1}{15} = \frac{5 + 4}{60} = \frac{9}{60} = \frac{3}{20} \)
Work done in 5 days = \( 5 \times \frac{3}{20} = \frac{15}{20} = \frac{3}{4} \)

4. Remaining Work and Time by B:

Remaining work = \( 1 - \frac{3}{4} = \frac{1}{4} \)
B’s 1 day work = \( \frac{1}{15} \)
Time = \( \frac{\frac{1}{4}}{\frac{1}{15}} = \frac{15}{4} = 3.75 \) days

Final Answer:

B will take 3.75 days (or 3 days and 3 hours) to finish the remaining work.