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 two people work together, their individual "rates of work" are added together. The rate of work is the reciprocal of the time taken to complete the job.

Step 2: Key Formula or Approach:
If A takes $x$ days and B takes $y$ days, the time taken together ($T$) is: \[ T = \frac{x \times y}{x + y} \]

Step 3: Calculation:
Substitute $x = 12$ and $y = 18$: \[ T = \frac{12 \times 18}{12 + 18} \] \[ T = \frac{216}{30} \] \[ T = 7.2 \text{ days} \]

Step 4: Final Answer:
They will complete the work together in 7.2 days.