CAT 2004 | Question: 54

Question

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?

• A. $130$ minutes
• B. $135$ minutes
• C. $170$ minutes
• D. $180$ minutes

 

Answer 1

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.