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A factory produces nuts and bolts. A machine in it produces only nuts 02 Dec 2020, 12:45
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46% (02:38) correct 54% (02:57) wrong based on 140 sessions

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A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 400 nuts per minute and need to be cleared for 15 minutes after production of 2000 nuts. The machine producing only bolts produces 300 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 12000 pairs of bolts and nuts if both machines are operated simultaneously.

A. 85 minutes
B. 100 minutes
C. 105 minutes
D. 115 minutes
E. 120 minutes
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C
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A factory produces nuts and bolts. A machine in it produces only nuts 04 Dec 2020, 03:21
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Bunuel
A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 400 nuts per minute and need to be cleared for 15 minutes after production of 2000 nuts. The machine producing only bolts produces 300 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 12000 pairs of bolts and nuts if both machines are operated simultaneously.

A. 85 minutes
B. 100 minutes
C. 105 minutes
D. 115 minutes
E. 120 minutes
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The machine producing nuts takes 2000/400 = 5 minutes for every 2000 bolts (assume it as 1 phase)

To produce 12,000 nuts, it will require 12000/2000 = 6 phases of 2000 bolts each = 6 * 5 = 30 minutes

Number of stops (2000 _ 2000 _ 2000 _ 2000 _ 2000 _ 2000) = 5. Stoppage time = 15 * 5 = 75 minutes.

Total Time here = 30 + 75 = 105 minutes


The machine producing nuts takes 3000/300 = 10 minutes for every 3000 bolts

To produce 12,000 bolts, it will require 12000/3000 = 4 phases of 3000 bolts = 4 * 10 = 40 minutes

Number of stops (3000 _ 3000 _ 3000 _ 3000 ) = 3. Stoppage time = 15 * 3 = 45 minutes.

Total time here = 40 + 45 = 85 minutes


Minimum time to make 12,000 pairs = Max (105, 85) = 105 minutes


Option C

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A factory produces nuts and bolts. A machine in it produces only nuts 12 Dec 2020, 09:03
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Bunuel
A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 400 nuts per minute and need to be cleared for 15 minutes after production of 2000 nuts. The machine producing only bolts produces 300 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 12000 pairs of bolts and nuts if both machines are operated simultaneously.

A. 85 minutes
B. 100 minutes
C. 105 minutes
D. 115 minutes
E. 120 minutes
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The minimum time will be limited with by the slowest machine.

The nuts machine produces 400 nuts every minute , so in 5 minutes it produces 2000 nuts.
So for 12000 nuts it will be require 30 minutes, with 15 minutes break every 5 minutes hence
5..15 .. 5 ... 15 ...5 ...15 ...5 ..15 ...5..15 ..5= total time ->5*6+ 15*5 = 105 minutes

The bolts machine produces 300 bolts very minute . so in 10 minutes it produces 3000 Bolts.
So for 12000 bolts , bolts machine will require 40 minutes, with 15 minutes break every 10 minutes so.
10..15..10..15..10..15..10= total time->10*4+15*3= 85 minutes

Hence 12000 pairs cannot possibly be completed in lesser than 105 minutes as this is the minimum time required by the nuts machine to complete 12000 Nuts.

Ans- C

Hope it's clear.
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A factory produces nuts and bolts. A machine in it produces only nuts 12 Dec 2020, 10:20
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Given: A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 400 nuts per minute and need to be cleared for 15 minutes after production of 2000 nuts. The machine producing only bolts produces 300 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts.
Asked: Find the minimum time required to produce 12000 pairs of bolts and nuts if both machines are operated simultaneously.

Time required by machine A to produce 2000 nuts = 5 mins + 15 mins rest
Time required by machine B to produce 3000 bolts = 10 mins + 15 mins rest

Time required by machine A to produce 12000 nuts = 5 + 15 + 5 + 15 + 5 + 15 + 5 + 15 + 5 + 15 + 5 = 30 + 75 = 105 mins
Time required by machine B to produce 12000 bolts = 10 + 15 + 10 + 15 + 10 + 15 + 10 = 40 + 45 = 85 mins

The minimum time required to produce 12000 pairs of bolts and nuts if both machines are operated simultaneously = max(105,85) = 105 mins


IMO C
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A factory produces nuts and bolts. A machine in it produces only nuts 29 Jun 2024, 23:19
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­For nuts machine:

Each batch of 2000 nuts require \(\frac{2000}{400}\) = 5 min with additional 15 min (clearance) 

Time required for 12000 nuts without clearances = \(12000/400\) = \(30\) \(minutes\)
But we've got interruptions of clearances = \(\frac{30}{5}\) = 6 times 
Last interruption doesn't count, so we got 5 intermittent interruptions accounting for \(5 * 15\) minutes = 75 minutes
Thus, total minimum time required to produce nuts = \(30\) \(minutes\) + \(75\) \(minutes\) = \(105\) \(minutes\)


For bolts machine:

Each batch of 3000 bolts require \(\frac{3000}{300}\) = 10 min with additional 15 minutes (clearance)

Time required for 12000 bolts without clearances = \(12000/300\) = \(40\) \(minutes\)
But we've got interruptions of clearances = \(\frac{40}{10}\) = 4 times 
Last interruption doesn't count, so we got 3 intermittent interruptions accounting for \(3 * 15\) minutes = 45 minutes
Thus, total minimum time required to produce bolts = 40 minutes + 45 minutes = 85 minutes

Worst case scenario = 105 minutes.

Answer is 105 \(minutes\).

 ­
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