Reena and Riya together can complete a piece of work in 36 days. Riya and Geeta together can complete it in 54 days. Reena and Geeta together can complete it in 81 days. In how many days can Reena alone complete the work?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. days.
Let the total work to be done (LCM of 36, 54 and 81) be 324 units.
Total work = Efficiency × Time taken
According to the given question,
Efficiency of Reena and Riya = 324/36 = 9 units/day
Efficiency of Riya and Geeta = 324/54 = 6 units/day
Efficiency of Reena and Geeta = 324/81 = 4 units/day
Efficiency of Reena, Riya and Geeta = 19/2 units/day
Efficiency of Reena = 19/2 - 6 = 7/2 units/day
Time taken by Reena alone = 324/(7/2)
⇒ 648/7 = days