Benny can do a piece of work in 24 days. Chethan and David can do the same work individually in 36 and 48 days, respectively. All of them begin the work together. However, Benny leaves the work 4 days before the completion of work and Chethan leaves the work 10 days before the completion of the work. David worked till the end and completed the work. Find the number of days in which the work was completed.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 16.
The Benny can do a piece of work = 24 days
One day's work of Benny = 1/24
The Chethan can do a piece of work = 36 days
One day's work of Chethan = 1/36
The David can do a piece of work = 48 days
One day's work of David = 1/48
Let the total number of days to complete the work = x
According to the question:
Work done by Benny = (x − 4) × 1/24
Work done by Chethan = (x − 10) × 1/36
Work done by David = x × 1/48
⇒ (x - 4)/24 + (x - 10)/36 + x/48 = 1
⇒ 6(x - 4)/144 + 4(x - 10)/144 + 3x/144 = 1
⇒ 6(x − 4) + 4(x − 10) + 3x = 144
⇒ 6x − 24 + 4x − 40 + 3x = 144
⇒ 13x − 64 = 144
⇒ x = 208/13 = 16 days