Anjali can do a certain piece of work in 20 days. Anjali and Ayushi can together do the same work in 16 days, and Anjali, Ayushi and Ankita can do the same work together in 10 days. In how many days can Anjali and Ankita do the same work?

Correct option is A

Given:

Anjali alone completes work in 20 days → rate = $$\frac 1{20}$$​​

Anjali + Ayushi complete in 16 days → rate = $$\frac 1{16}$$​​

Anjali + Ayushi + Ankita complete in 10 days → rate =$$\frac 1{10}$$​​

Formula Used:
Work rate = $$\frac1{\text{Time}}$$​​

Solution:
Ayushi’s rate = $$\frac1{16} – \frac1{20} = \frac1{80}$$​​

Ankita’s rate  = $$\frac1{10} – \frac1{16} =\frac 3{80}$$​​
Anjali + Ankita =$$\frac 1{20} + \frac3{80} =\frac 7{80}$$​​
Time =$$\frac{{1}}{\frac{7}{80}}=\frac{80}7$$​days 

​Alternate Method:

Efficiency of Ankita = 8 - 5 = 3 

Efficiency of Anjali = 4

​Anjali and Ankita can do the work = $$\frac {80}{4+3}=\frac{80}7$$ days​