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

The objective is to determine the duration B requires to complete the outstanding work after a period of collaboration with A.

1. Foundational Principles:

- Work Rate: An individual completing a task in 'n' days has a daily work contribution of \( \frac{1}{n} \).
- Aggregate Effort: When multiple individuals collaborate, their combined daily work is the sum of their individual daily contributions.
- Unfinished Work: This is calculated by subtracting the work already completed from the total task (considered as 1 unit).

2. Provided Data:

- A's work completion time: 12 days → A's daily work rate = \( \frac{1}{12} \)
- B's work completion time: 15 days → B's daily work rate = \( \frac{1}{15} \)
- Joint work duration: 5 days

3. Calculation of Joint Work Accomplished:

Combined daily work rate = \( \frac{1}{12} + \frac{1}{15} = \frac{5 + 4}{60} = \frac{9}{60} = \frac{3}{20} \)
Work completed over 5 days = \( 5 \times \frac{3}{20} = \frac{15}{20} = \frac{3}{4} \)

4. Determination of Remaining Work and B's Timeframe:

Remaining work = \( 1 - \frac{3}{4} = \frac{1}{4} \)
B's daily work rate = \( \frac{1}{15} \)
Time required by B = \( \frac{\frac{1}{4}}{\frac{1}{15}} = \frac{15}{4} = 3.75 \) days

Conclusion:

B will require 3.75 days (equivalent to 3 days and 3 hours) to finalize the remaining portion of the task.