Question

A can complete a work in 12 days and B can complete it in 18 days. In how many days will they complete the work together?

• A. 6 days
• B. 7.2 days
• C. 8 days
• D. 9 days

Hint:

When two people work together, the total time will always be less than the time taken by the fastest person alone. Since A takes 12 days, the answer must be less than 12 (which all options are, but it's a good sanity check!).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When people work together, their daily work rates are added to determine the combined efficiency.
Rate is the inverse of the time taken to complete the task.
Step 2: Key Formula or Approach:
If A takes \( x \) days and B takes \( y \) days, the time taken together (\( T \)) is:
\[ T = \frac{xy}{x+y} \] Alternatively, you can add their one-day work: \( \frac{1}{x} + \frac{1}{y} = \frac{1}{T} \).
Step 3: Detailed Explanation:
Given values:
Time for A (\( x \)) = 12 days.
Time for B (\( y \)) = 18 days.
Using the shortcut formula:
\[ T = \frac{12 \times 18}{12 + 18} \] \[ T = \frac{216}{30} \] Simplify the fraction:
\[ T = \frac{216 \div 3}{30 \div 3} = \frac{72}{10} \] \[ T = 7.2 \text{ days} \] So, working together, they take 7.2 days to complete the job.
Step 4: Final Answer:
They will complete the work together in 7.2 days.