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05 Sep 2024, 02:42
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Machine A is run for 1 minute, then shutdown for 17 minutes then again run for 1 minute....and this cycle continues. Basically, Machine A restarts every 18th minute (for a total of 1 minute) and each time Machine A is run, it consumes 15 units of power.................Similarly, B restarts every 15th minute while consuming 18 units of power........and C restarts every 12th minute while consuming 12 units of power
The simplified question is, at what exact moment while the power consumption exceed 30 units? Neither machine consumes more than 30 units. It means a combination of machines should start together, at the exact same time! A + B = 15+18 = 33 units (> 30 units). So if A + B starts together, we need that backup generator! A + C = 15 + 12 = 27 units (< 30 units)...so we don’t need the backup generator. B + C = 18 + 12 = 30 units (=30 units)....so in this case too, we don’t need the backup generator....And lastly, A + B + C = 15 + 12 + 18 = 45 units, so we definitely need the backup generator.
So the question is reduced to, "When will Machine A and Machine B simultaneously start?"....because if they do, we would need to use the backup generator. A restarts in every 18th minute and B in every 15th minute....so simultaneously they’ll restart every LCM (18,15) = 90th minute. Hence, after every 90 minutes, Machine A and B will start together, use 33 units of power exceeding the limit of 30 units and requiring the backup generator to give power. Answer is (C) 90 minutes.
The simplified question is, at what exact moment while the power consumption exceed 30 units? Neither machine consumes more than 30 units. It means a combination of machines should start together, at the exact same time! A + B = 15+18 = 33 units (> 30 units). So if A + B starts together, we need that backup generator! A + C = 15 + 12 = 27 units (< 30 units)...so we don’t need the backup generator. B + C = 18 + 12 = 30 units (=30 units)....so in this case too, we don’t need the backup generator....And lastly, A + B + C = 15 + 12 + 18 = 45 units, so we definitely need the backup generator.
So the question is reduced to, "When will Machine A and Machine B simultaneously start?"....because if they do, we would need to use the backup generator. A restarts in every 18th minute and B in every 15th minute....so simultaneously they’ll restart every LCM (18,15) = 90th minute. Hence, after every 90 minutes, Machine A and B will start together, use 33 units of power exceeding the limit of 30 units and requiring the backup generator to give power. Answer is (C) 90 minutes.
26 Sep 2025, 07:08
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I struggled badly in one aspect of this question:
It is asking for the sum of power usage at any instant in time to be >30 units. It isn't the case that the units used are added or tracked.
For example, when we say all three start together, at the 18th minute, the power usage is 15 units (from Machine A alone), and not 45 units (12+18+15 units from each machine up until this 18th minute).
I am not sure why I thought the latter was the case.
It is asking for the sum of power usage at any instant in time to be >30 units. It isn't the case that the units used are added or tracked.
For example, when we say all three start together, at the 18th minute, the power usage is 15 units (from Machine A alone), and not 45 units (12+18+15 units from each machine up until this 18th minute).
I am not sure why I thought the latter was the case.
parkhydel
