Rohit, Mohit and Sumit individualy can complete a work in 8 days, 14 days and 21 days respectively. In how many days these three together can complete the same work?

Options

A. 156/43 days
B. 168/41 days
C. 168/43 days
D. 156/41 days

Answer

To solve the problem, we need to find out how much work Rohit, Mohit, and Sumit can complete together in one day, and then determine how many days it will take them to complete the entire work.

### Step-by-Step Solution:

1. **Determine Individual Work Rates:**
- Rohit can complete the work in 8 days. Therefore, his work rate is:
\[ \text{Rohit's work rate} = \frac{1}{8} \text{ of the work per day} \]
- Mohit can complete the work in 14 days. Therefore, his work rate is:
\[ \text{Mohit's work rate} = \frac{1}{14} \text{ of the work per day} \]
- Sumit can complete the work in 21 days. Therefore, his work rate is:
\[ \text{Sumit's work rate} = \frac{1}{21} \text{ of the work per day} \]

2. **Calculate Combined Work Rate:**
- To find the total work rate when all three work together, we add their individual work rates:
\[ \text{Total work rate} = \frac{1}{8} + \frac{1}{14} + \frac{1}{21} \]

3. **Find a Common Denominator:**
- The least common multiple (LCM) of 8, 14, and 21 is 168. We will convert each fraction to have this common denominator:
\[ \frac{1}{8} = \frac{21}{168}, \quad \frac{1}{14} = \frac{12}{168}, \quad \frac{1}{21} = \frac{8}{168} \]

4. **Add the Fractions:**
- Now we can add the fractions:
\[ \text{Total work rate} = \frac{21}{168} + \frac{12}{168} + \frac{8}{168} = \frac{41}{168} \]

5. **Calculate Time to Complete the Work:**
- The total work rate of \(\frac{41}{168}\) means that together they complete \(\frac{41}{168}\) of the work in one day. To find out how many days it takes to complete the entire work, we take the reciprocal of the total work rate:
\[ \text{Days to complete the work} = \frac{1}{\frac{41}{168}} = \frac{168}{41} \approx 4.1 \text{ days} \]

### Final Answer:
Thus, Rohit, Mohit, and Sumit together can complete the work in approximately **4.1 days**.