Question : 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.
Option 1: 24
Option 2: 27
Option 3: 30
Option 4: 25
Correct Answer: 27
Solution :
Let the total work = LCM (36, 48, and 144) = 144
According to the question,
Efficiency of P = $\frac{144}{36}$ = 4
Efficiency of Q = $\frac{144}{48}$ = 3
Efficiency of R = $\frac{144}{144}$ = 1
Additional work P could have done if not left = 4 × 12 = 48
Additional work Q could have done if not left = 3 × 8 = 24
Now,
Effective total work = 144 + 48 + 24 = 216
$\therefore$ Time taken = $\frac{\text{Total work}}{\text{Efficiency}}$ = $\frac{216}{8}$ = 27 days
Hence, the correct answer is 27.
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