Question
Priya can do a certain piece of work in 30 days. Priya and Varsha can together do the same work in 18 days, and Priya, Varsha, and Nisha can do the same work together in 9 days. In how many days can Priya and Nisha do the same work?
The correct answer is
45/4
Let the rates of Priya, Varsha, and Nisha be p, v, and n, respectively. We know that Priya can complete the work in 30 days, so her rate is 1/30. Priya and Varsha together can complete it in 18 days, so their combined rate is 1/18. Similarly, Priya, Varsha, and Nisha together can complete it in 9 days. From this, we can set up equations and solve to find the time taken by Priya and Nisha together.
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Important Questions from Time and Work
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