GATE 2017 CE (CE1) – Question 9

General Aptitude · Analytical Aptitude: Logical Reasoning, Deduction and Analogy · 2 marks · Multiple choice

Machines M1 and M2 can each perform any one of jobs P, Q, R, S on one object at a time. Their processing times are 30, 20, 60, 15 minutes respectively. Ten objects each need exactly one job: P on 2, Q on 3, R on 1 and S on 4 objects. What is the minimum completion time?

2 hours
2.5 hours
3 hours
3.5 hours

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Correct answer: (A) 2 hours

Explanation

The total workload is $2(30)+3(20)+1(60)+4(15)=240$ machine-minutes. Two machines therefore need at least 120 minutes. This bound is attainable: M1 performs R and both P jobs, totaling $60+30+30=120$; M2 performs all Q and S jobs, totaling $3(20)+4(15)=120$. The minimum is 2 hours, A.

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