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Let total work be W Then work done by one machine in one day = W/(12X6)
Let n machines be required for 8 days total work done = W/(12X6) X n X 8 which should be again W hence n = 9 so 3 more machines are required to complete the the work in 8 days.
Alternatively:
W is directly proportional to number of machines and number of days
thus 12X 6 = n X 8 implies n=9 thus 3 more are required.
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