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In Nuts and Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for five minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start the production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

1. 130 minutes
2. 135 minutes
3. 170 minutes
4. 180 minutes

+1 vote
N-Nuts  B-Bolts M-Minute

100 N/M so to produce 1000 N ->>10 Min

Then 5 min for cleaning so total 10+5=15 min (for 1000 Nut production & Cleaning)

To produce 8000 N it will take  8 times 15 min =120 min

Now to produce next 1000 N it'll take only 10 min (No need to clean)

So 120+10=130 Min to produce 9000/Nuts

Now Come to Bolt(B)

75 B/M so to produce 1500B ->>(1500/75)=20 Min

Then 10 min for cleaning so total 20+10=30min (for 1500 Bolt production & Cleaning)

To produce 7500 B it will take 5 times 30 min=150min

Now to produce next 1500 B it'll take only 20 min (No need to clean)

So 150+20=170 Min to produce 9000/Bolts

Now as given in Question both production are done simultaneously So to produce 9000 Bolts and nuts it will take minimum time= max(9000 Nut production time, 9000 Bolt production time)=(130 min ,170 min)=170 min

So, Option(3) is Ans.