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Select the correct answerA factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously?Options20 minutes32 minutes25 minutes40 minutes

Question

Select the correct answerA factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously?Options20 minutes32 minutes25 minutes40 minutes

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Solution

To solve this problem, we need to calculate the time required for each machine to produce the required number of nuts and bolts.

  1. For the nuts machine: It produces 500 nuts per minute, so to produce 6000 nuts, it would take 6000/500 = 12 minutes. However, the machine needs to be cleared for 10 minutes after every 2000 nuts. So, for 6000 nuts, it needs to be cleared 3 times, adding an extra 3*10 = 30 minutes. Therefore, the total time for the nuts machine is 12 + 30 = 42 minutes.

  2. For the bolts machine: It produces 600 bolts per minute, so to produce 6000 bolts, it would take 6000/600 = 10 minutes. The machine needs to be cleared for 15 minutes after every 3000 bolts. So, for 6000 bolts, it needs to be cleared 2 times, adding an extra 2*15 = 30 minutes. Therefore, the total time for the bolts machine is 10 + 30 = 40 minutes.

Since both machines are operated simultaneously, the minimum time required to produce 6000 pairs of bolts and nuts is the maximum of the two times calculated, which is 42 minutes. However, this option is not available in the given options. There might be a mistake in the problem or the options provided.

This problem has been solved

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