Question

A and B can do a work in 12 days and 15 days respectively. How long will they take to complete the work if they work together?

• A. 6\(\frac{2}{3}\) days
• B. 7 days
• C. 8 days
• D. 5 days

Hint:

In work and time problems, calculate each person’s work rate (work per day = 1/time taken). Add the rates to find the combined rate, then take the reciprocal to find the total time. Use the least common multiple (LCM) of individual times to simplify calculations or verify results. If the result is not a whole number, check the options for the closest reasonable value or consider if the problem assumes completion in whole days.

Answer 1

The Correct Option is A

To solve the problem, we need to find the time taken by A and B working together to complete the work.

1. Understanding the Concepts:

- Work Rate: If A can complete the work in 12 days, A's 1 day work = \( \frac{1}{12} \)
- Similarly, B's 1 day work = \( \frac{1}{15} \)
- When working together, their combined 1 day work = sum of individual 1 day works.
- Total time taken together = reciprocal of combined 1 day work.

2. Given Values:

- A's time = 12 days
- B's time = 15 days

3. Calculate Combined Work Rate and Time:

\[ \text{Combined work rate} = \frac{1}{12} + \frac{1}{15} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20} \] \[ \text{Time taken} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{3}{20}} = \frac{20}{3} = 6\frac{2}{3} \text{ days} \]

Final Answer:

A and B working together will complete the work in 6\(\frac{2}{3}\) days or 6 days and 8 hours.