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10 Jan 2024, 22:21
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B
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Difficulty:
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Question Stats:
81% (02:32) correct
19%
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Machine K and Machine N, working simultaneously and independently at their respective constant rates, process 2/3 of the shipment of a certain chemical product in 1.6 hours. Then machine K stopped working, and Machine N, working alone at it's constant rate, processed the rest of the shipment in 2 hours. How many hours would it have taken Machine K, working alone at its constant rate, to process the entire shipment?
A. 3.8
B. 4.0
C. 4.8
D. 5.4
E. 6.0
2024-01-30_19-48-44.png [ 66.9 KiB | Viewed 8461 times ]
A. 3.8
B. 4.0
C. 4.8
D. 5.4
E. 6.0
Attachment:
2024-01-30_19-48-44.png [ 66.9 KiB | Viewed 8461 times ]
10 Jan 2024, 23:55
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AnkurGMAT20
Machine K and Machine N, working simultaneously and independently at their respective constant rates, process 2/3 of the shipment of a certain chemical product in 1.6 hours.
Inference: To process \(\frac{2}{3}^{\text{rd}}\) of the shipment, Machine K and Machine N, working simultaneously and independently at their respective constant rates, take \(1.6\) hours. Hence, to process the entire shipment the machines would have taken \(\frac{3}{2}^{\text{rd}}\) the time taken to process \(\frac{2}{3}^{\text{rd}}\) of the shipment.
To process \(\frac{2}{3}^{\text{rd}}\) unit of the shipment ----------------- \(1.6\) hours
To process \(1\) unit of the shipment ----------------- \(1.6 * \frac{3}{2} = 2.4\) hours
Then machine K stopped working, and Machine N, working alone at it's constant rate, processed the rest of the shipment in 2 hours
Inference: Hence, machine N processed the remaining \(\frac{1}{3}^{\text{rd}}\) shipment in 2 hours. Therefore, to process the entire shipment alone, machine K would have taken thrice the time taken to process \(\frac{1}{3}^{\text{rd}}\) shipment.
To process \(\frac{1}{3}^{\text{rd}}\) unit of the shipment Machine K, working alone, took ----------------- \(2\) hours
To process \(1\) unit of the shipment Machine K, working alone, will take ----------------- \(2 * 3 = 6\) hours
If Machine N, working alone at its constant rate, takes \(T_1\) hours to complete one unit of task and Machine K, working alone at its constant rate, takes \(T_2\) hours to complete one unit of the same task, the time taken by Machine K and Machine N, working simultaneously and independently at their respective constant rates, to complete one unit of task is given by -
\(T_{\text{together}} = \frac{T_1 * T_2}{T_1 + T_2}\)
In this question -
- \(T_{\text{together}} = 2.4\) hours
- \(T_1 = 6\) hours
- \(T_2 =\) ?
Substituting the values in the above formula
\(2.4 = \frac{6T_2}{6 + T_2}\)
\(14.4 + 2.4T_2 = 6T_2\)
\(3.6T_2 = 14.4\)
\(T_2 = \frac{14.4}{3.6} = 4.0\)
Option B
11 Jan 2024, 00:35
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AnkurGMAT20
Machine N, working alone, in 2 hours processed \(1 - \frac{2}{3} = \frac{1}{3}\) of the shipment. Hence, in 1.6 hours, it processed \((time)*(rate) = 1.6*\frac{(\frac{1}{3})}{2} = \frac{4}{5}*\frac{1}{6} = \frac{4}{15}\) of the shipment.
Thus, in 1.6 hours, the remaining \(\frac{2}{3} - \frac{4}{15} = \frac{2}{5}\) of the shipment was processed by Machine K. Therefore, to process the entire shipment alone, Machine K would take \(\frac{1}{(\frac{2}{5})}*1.6 = \frac{5}{2}*\frac{8}{5} = 4\) hours.
Answer: B
