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?

Correct option is B

Given:

Priya alone = 30 days

Priya + Varsha = 18 days

Priya + Varsha + Nisha = 9 days

Find: Time taken by Priya + Nisha

Formula Used:

Efficiency = Total Work / Time

Solution:

LCM of 30, 18, 9LCM = 90 units (Total Work)

Priya’s efficiency = 90/30 = 3 units/day

Priya + Varsha efficiency = 90/18 = 5 units/day

Varsha’s efficiency = 5 − 3 = 2 units/day

Priya + Varsha + Nisha efficiency = 90/9 = 10 units/day

Nisha’s efficiency = 10 − (3 + 2) = 5 units/day

Priya + Nisha efficiency

= 3 + 5 = 8 units/day

Required time = 90 / 8

= 45/4 days