Shifa can do a certain piece of work in 22 days. Shifa and Afiya can together do the same work in 18 days, and Shifa, Afiya and Mariyam can do the same work together in 9 days. In how many days can Shifa and Mariyam do the same work?

Correct option is A

Given:
Shifa alone can do the work in 22 days
Shifa + Afiya can do it in 18 days
Shifa + Afiya + Mariyam can do it in 9 days
Formula Used:
Work = LCM of all days
Efficiency = Work ÷ Time
Solution:
Total Work = LCM(22, 18, 9) = 198 units
=> Shifa's 1 day work =$$\frac{198}{22}$$​ = 9 units/day
=> Shifa + Afiya's 1 day work =$$\frac{198}{18}$$​ = 11 units/day
=> Afiya's 1 day work = 11 - 9 = 2 units/day
=> Shifa + Afiya + Mariyam's 1 day work = 198 ÷ 9 = 22 units/day
=> Mariyam's 1 day work = 22 - (Shifa + Afiya) = 22 - 11 = 11 units/day
=> Shifa + Mariyam's 1 day work = 9 + 11 = 20 units/day
=> Time to finish 198 units = $$\frac{198}{20} = \frac {99}{10}$$​days 
∴ Shifa and Mariyam together can do the work in $$\frac{99}{10}$$ days​