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?
Show Hint
6\(\frac{2}{3}\) days
- 7 days
- 8 days
- 5 days
The Correct Option is A
Solution and Explanation
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.
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