A speaker talked for sixty minutes to a full auditorium. Twenty percent of the audience heard the entire talk and ten percent slept through the entire talk. Half of the remainder heard one third of the talk and the other half heard two thirds of the talk. What was the average number of minutes of the talk heard by members of the audience?
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By the question we have,
20% heard 60 minutes.
10% heard 0 minutes.
Half the remainder , = 2 7 0 % = 3 5 % heard 20 minutes
And the other 35% heard 40 minutes.
Therefore average number of minutes heard = 2 0 % × 6 0 + 1 0 % × 0 + 3 5 % × 2 0 + 3 5 % × 4 0
= 0 . 2 × 6 0 + 0 + . 3 5 × 2 0 + . 3 5 × 4 0
= 1 2 + 7 + 1 4
= 3 3