John, Johnny and Janardan can finish a task in a field in 6, 12, and 24 days, respectively. In how many days will they finish the task working together?

Correct option is C

​Given:

John finish task in 6 days

Johnny finish task in 12 days

Janardan finish task in 24 days

Formula Used:
Rate together = John’s rate + Johnny’s rate + Janardan’s rate

​​Time to complete 1 job:

​$$\text{Time} = \frac{1}{\text{Rate Together}}$$​​

Solution:

John’s rate = $$\frac{1}{6} \, \text{jobs/day}$$​​

Johnny’s rate = $$\frac{1}{12} \, \text{jobs/day}$$​​

Janardan’s rate = $$\frac{1}{24} \, \text{jobs/day}$$ 

Their combined work rate;

​$$\text{Rate Together} = \frac{1}{6} + \frac{1}{12} + \frac{1}{24}$$ 

​$$\text{Rate Together} = \frac{4}{24} + \frac{2}{24} + \frac{1}{24} = \frac{7}{24}$$ 

$$\text{Rate Together} = \frac{4}{24} + \frac{2}{24} + \frac{1}{24} = \frac{7}{24}$$  

Time to complete the work together;

​$$\text{Time} = \frac{1}{\frac{7}{24}} = \frac{24}{7} = 3\frac{3}{7} \ days$$​​