A can do a piece of work in 4 days and B can do it in 12 days. In how many days will they finish the work, both working together?
A एक कार्य को 4 दिन में कर सकता है और B उसे 12 दिन में कर सकता है। दोनों मिलकर उस कार्य को कितने दिन में पूरा करेंगे?

Options

A. 3 day / 3 दिन
B. 4 day / 4 दिन
C. 6 day / 6 दिन
D. 2 day / 2 दिन

Explanation

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

### Step-by-Step Solution:

1. **Determine the Work Done by A and B Individually**:
- A can complete the work in 4 days.
- B can complete the work in 12 days.

2. **Calculate the Work Done per Day**:
- Work done by A in one day = 1/4 of the work.
- Work done by B in one day = 1/12 of the work.

3. **Find the Combined Work Done in One Day**:
- To find the total work done by A and B together in one day, we add their individual work rates:
\[ \text{Combined work per day} = \frac{1}{4} + \frac{1}{12} \]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 4 and 12 is 12.
- Convert \(\frac{1}{4}\) to have a denominator of 12:
\[ \frac{1}{4} = \frac{3}{12} \]
- Now, add the fractions:
\[ \frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3} \]
- Therefore, A and B together can complete \(\frac{1}{3}\) of the work in one day.

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

### Final Answer:
A and B together will finish the work in **3 days**.

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