In Nuts And Bolts 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?
Explanation:
100 nuts are produced per minute. ∴ Time taken to produce 1000 nuts = 10 minutes. But the machine needs cleaning for 5 minutes after producing 1000 nuts. Thus effective time taken to produce 1000 nuts = 15 minutes. Effective time taken to produce 9000 nuts = 9 × 15 – time taken for the last cleaning = 135 – 5 = 130 minutes.
75 bolts are produced per minute. ∴ Time taken to produce 1500 bolts = 20 minutes. But the machine needs cleaning for 10 minutes after producing 1500 bolts. Thus effective time taken to produce 1500 bolts = 30 minutes. Effective time taken to produce 9000 bolts = 6 × 30 – time taken for the last cleaning = 180 – 10 = 170 minutes.
Thus time taken to produce 9000 pairs of nuts and bolts = 170 minutes.
Hence, option (c).
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