Riya can complete a piece of work in 12 days, Reeta in 18 days and Geeta in 24 days. Reeta and Geeta worked together for 6 days and then Geeta was replaced by Riya. In how many days altogether was the work completed?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 9 days
As we know that
Worker × time = Total work
Given that
Riya can do a work in 12 days
Reeta can do a work in 18 days
Geeta can do a piece of work in 24 days
Total work = LCM (12, 18, 24) = 72
The efficiencies of Riya, Reeta and Geeta are
⇒ (72/12 = 6), (72/18 = 4), and (72/24 = 3)
According to the question
⇒ (Reeta + Geeta) × 6 + (Reeta + Riya) × d = 72
⇒ (4 + 3) × 6 + (4 + 6) × d = 72
⇒ 42 + 10d =72
⇒ 10d = 30
⇒ d = 3 days
Hence, the work is completed altogether in 6 + 3 = 9 days