P, Q, and R, when working individually, can complete a job in, respectively, 36 days, 48 days, and 144 days. P, Q, and R start working together. P leaves the job 12 days before completion and Q leaves the job 8 days before completion. R works from the beginning till the end of the job. Determine the total number of days taken to complete the job.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 27.
P, Q, and R, when working individually, can complete a job in, respectively, 36 days, 48 days, and 144 days
Total work (L.C.M of 36, 48, and 144) = 144
The efficiency of P = 144/36 = 4 units
The efficiency of Q = 144/48 = 3 units
The efficiency of R = 144/144 = 1 units
Let n days are required to complete the work
⇒ 4(n - 12) + 3(n - 8) + 1n = 144
⇒ 4n - 48 + 3n - 24 + n = 144
⇒ 8n - 72 = 144
⇒ 8n = 216
⇒ n = 27