Given Lasya can do a work in 16 days.
Now, time taken by Srimukhi alone to complete the work = 16 x 100/80
Time taken by Rashmi = n days
=> (12 x 20)/(20 - 12) = (12 x 20)/n
=> n= 30 days.
Required ratio of efficiencies of Rashmi and Lasya = 1/30 :: 1/16 = 8 : 15.