Multiple choice

A task la done by 46 persons not all of them have the same capacity to task. Every day exactly 2 persons,do the task with no pair of persons working together twice. Even after all possible pairs have worked once, all the persons together work for two more days to finish the task. Find the number of days in which all the persons together will finish the whole task?

  1. 44

  2. 45

  3. 46

  4. 47

  5. None of these
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D Correct answer
AI explanation

The number of unique pairs that can be formed from 46 persons is 46 multiplied by 45 divided by 2, which equals 1035 pairs. Let the sum of the daily capacities of all 46 persons be S; the total work completed by the pairs over 1035 days is 1035 multiplied by 2 and then divided by 46, resulting in 45S. Working together for 2 more days, the 46 persons complete an additional 2S, making the total work 47S. Since the 46 persons complete 1S per day together, they would take exactly 47 days to finish the entire task.

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