A can do a piece of work in 4 days and B can complete the same work in 12 days. What is the number of days required to do the same work together?

Options

A. 2 days
B. 3 days
C. 4 days
D. 5 days

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-by-Step Solution:

1. **Determine the work done by A in one day:**
- A can complete the work in 4 days. Therefore, the work done by A in one day is:
\[ \text{Work done by A in one day} = \frac{1}{4} \]

2. **Determine the work done by B in one day:**
- B can complete the work in 12 days. Therefore, the work done by B in one day is:
\[ \text{Work done by B in one day} = \frac{1}{12} \]

3. **Calculate the combined work done by A and B in one day:**
- When A and B work together, their combined work done in one day is:
\[ \text{Combined work} = \frac{1}{4} + \frac{1}{12} \]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 4 and 12 is 12. We can convert \(\frac{1}{4}\) to have a denominator of 12:
\[ \frac{1}{4} = \frac{3}{12} \]
- Now we can add:
\[ \frac{3}{12} + \frac{1}{12} = \frac{4}{12} \]
- Simplifying \(\frac{4}{12}\):
\[ \frac{4}{12} = \frac{1}{3} \]

4. **Determine the total number of days required to complete the work together:**
- If A and B together complete \(\frac{1}{3}\) of the work in one day, then the total number of days required to complete the entire work is the reciprocal of \(\frac{1}{3}\):
\[ \text{Total days} = \frac{1}{\frac{1}{3}} = 3 \]

### Final Answer:
A and B together will take **3 days** to complete the work.

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