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NutsAndBolts

by shashank.ism » Tue Feb 09, 2010 7:24 am
In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 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 production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

130 minutes
135 minutes
170 minutes
180 minutes
200 minutes
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by Osirus@VeritasPrep » Tue Feb 09, 2010 12:21 pm
It would take 170 minutes.

Since bolts are produced at the slower rate, you only need to calculate how long it would take to produce 9000 bolts and include the time for breaks.

First, convert 75bolts per minute into 1500 bolts per hour. Next use the W = R X T formula. It would take divide 9000 by 4500 and you are left with 2 hours which translates to 120 minutes. However, you need to calculate how many breaks the machine would need. The machine needs to be cleaned for ten minutes for every 1500 bolts. Divide 9000 by 1500. The result is six, but one of these times would be after the job is done, so we don't calculate this break. So the machine must be cleaned for 10 minutes 5 times, which is 50 minutes. Add 50 mintutes to 120 and you arrive at your answer 170 minutes.
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by komal » Tue Feb 16, 2010 11:43 am
shashank.ism wrote:In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 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 production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

130 minutes
135 minutes
170 minutes
180 minutes
200 minutes
Time taken in producing 9000 nuts

= 9000/100 × 1 + 9000/1000 × 5

= 90 + 45 = 135 minutes

Time taken in producing 9000 bolts

= 9000/75 × 1 + 9000/1500 × 10

= 120 + 60 = 180 minutes

Thus for making 9000 pairs of nuts and bolts time taken is 180 minutes.
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by ajith » Tue Feb 16, 2010 2:07 pm
komal wrote: Time taken in producing 9000 nuts

= 9000/100 × 1 + 9000/1000 × 5

= 90 + 45 = 135 minutes

Time taken in producing 9000 bolts

= 9000/75 × 1 + 9000/1500 × 10

= 120 + 60 = 180 minutes

Thus for making 9000 pairs of nuts and bolts time taken is 180 minutes
The time taken for producing a lot of 1500 bolts is 20 minutes
after that there is a 10 minutes break

it takes 6 lots of 1500 to make it 9000
we need 5 breaks in between these lots
time taken = 6*20+50 = 170 as Osirus mentioned
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