Ram can complete a piece work in 15 days, Rohan in 25 days, and Rohit in 30 days. Rohan and Rohit worked together for 2 days and then Rohit was replaced by Ram. In how many days altogether was the work completed?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10 days.
Ram can complete the work = 15 days
so Ram's work per day = 1/15
Rohan can complete the work = 25 days
so Rohan's work per day = 1/25
Rohit can complete the work = 30 days
so Rohit's work per day = 1/30
The combined work done by Rohan and Rohit in 1 day = 1/25 + 1/30 = 11/150
In 2 days, Rohan and Rohit will complete = 2 × 11/150 = 22/150 = 11/75
Total work = 1
Work left after 2 days is: 1 − 1/175 = 75/75 − 11/75 = 64/75
The combined work done by Rohan and Ram in 1 day = 1/25 + 1/15 = 8/75
The number of days required to complete the remaining work = (64/75)/(8/75)
⇒ 64/75 × 75/8 = 64/8 = 8 days
Thus, the total time taken to complete the work = 2 + 8 = 10 days