If A can do a work in 10 days and B can do the same work in 15 days, then how many days will they take to complete the work both while working together?

Answer

To solve the problem of how many days A and B will take to complete the work together, we can follow these steps:

### Step 1: Determine the work done by A and B individually.
- A can complete the work in 10 days.
- B can complete the work in 15 days.

### Step 2: Calculate the work done by A and B in one day.
- Work done by A in one day = 1/10 of the work.
- Work done by B in one day = 1/15 of the work.

### Step 3: Find a common denominator to add the work done by A and B.
- The least common multiple (LCM) of 10 and 15 is 30.
- Work done by A in one day = 3/30 (since 1/10 = 3/30).
- Work done by B in one day = 2/30 (since 1/15 = 2/30).

### Step 4: Add the work done by A and B together.
- Total work done in one day by A and B together = (3/30 + 2/30) = 5/30 = 1/6 of the work.

### Step 5: Calculate the total time taken to complete the work together.
- If A and B together complete 1/6 of the work in one day, then they will take 6 days to complete the entire work.

### Final Answer:
A and B will take 6 days to complete the work when working together.

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