Final answer:
By setting up and solving equations based on the work contributions of Sonal and Preeti, we find that Preeti would take 60 days to complete the project by herself.
Step-by-step explanation:
To solve the problem of finding how many days it would take Preeti to complete the entire project by herself, we need to consider the work done by both Sonal and Preeti as part of a whole. Let's denote the work done in one day by Preeti as P and the work done in one day by Sonal as S. Since they can complete the project together in 30 days, we can write the equation 1 project = 30(S + P).
Given Sonal worked for 16 days and Preeti completed the remaining work in 44 days, we can say that the work Sonal did is 16S and the work Preeti did is 44P. Summing these contributions, we can equate them to the whole project: 16S + 44P = 1 project.
We know from the first equation that 30(S + P) = 1 project, so dividing both sides of this equation by 30 gives us S + P = 1/30. Multiplying both sides of this by 16 gives us 16S + 16P = 16/30.
Subtracting this equation from the equation regarding Sonal's and Preeti's work contributions, 16S + 44P = 1 project, we get (16S + 44P) - (16S + 16P) = 1 - 16/30, simplifying to 28P = 14/30. Therefore, P = 14/(30*28) = 1/60.
If Preeti alone can complete 1/60 of the project in a day, it will take her 60 days to complete the entire project by herself. Thus, the correct answer is C. 60 Days.