Kapil, Mohan, and Raju can do a piece of work separately in 18, 36, and 54 days. They started the work together, but Mohan left the work 8 days before the completion of the work, and Raju left the work 6 days before the completion of the work. Find the (approximate) time in which the work is completed.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 13 days
Given that
Kapil can do some work alone for 18 days
Mohan can do some work alone for 36 days
Raju can do some work alone for 54 days
Total work = LCM (18, 36, 54) = 108
The efficiency of the Kapil = 108/18 = 6
The efficiency of the Mohan = 108/36 = 3
The efficiency of the Raju = 108/54 = 2
Let Kapil work for D days
According to the question
⇒ Mohan × (D - 8) + Kapil × D + Raju × (D - 6) = 108
⇒ 3 × (D - 8) + 6 × D + 2 × (D - 6) = 108
⇒ 3D - 24 + 6D + 2D - 12 = 108
⇒ 11D = 108 + 36 = 144
⇒ D = 144/11 = 13.09 ≈ 13 (approximate)