Sita can clean a hotel in 20 days. Rita can clean the same hotel in 30 days. How many days will they take to clean the hotel together?

Correct option is B

​Given:

Sita clean hotel in 20 days​​

Rita clean hotel in 30 days

Formula Used:
Combined rate:

​Rate Together = Sita’s rate + Rita’s rate

Time to complete 1 hotel:

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

Solution:

Sita’s rate = $$\frac{1}{20} \, \text{hotels/day}$$​​

Rita’s rate = $$\frac{1}{30} \, \text{hotels/day}$$ 

Combine work rate together 

​$$\text{Rate Together} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}$$ 

So , time taken by Sita + Rita together 

$$\text{Time} = \frac{1}{\frac{1}{12}} = 12 \, \text{days}$$​​