A speaker talked for 60 minutes to a full auditorium. Twenty percent of the atte

Question

A speaker talked for 60 minutes to a full auditorium.

Twenty percent of the attendees listened to the entire presentation while ten percent slept through the entire talk.

Divide the remaining attendees in half.

The first half is called Group A and the second half is called Group B.

1) Suppose Group A heard one-third of the talk and Group B heard two-thirds of the talk. What is the average number of minutes of the talk heard by all members of the audience?

2) Suppose Group A heard one-fourth of the lecture Group B heard three-fourths of the lecture. What is the average number of minutes of the talk heard by all members of the audience?

3) Suppose Group A heard one-fifth of the lecture Group B heard four-fifths of the lecture. What is the average number of minutes of the talk heard by all members of the audience?

4) Following the same pattern, what is the average number of minutes of the talk heard by members of the audience if Group A heard one-nth of the lecture and Group B heard the portion of the lecture not heard by Group A? Explain your reasoning.

5) Suppose thirty percent of the attendees listened to the entire talk, ten percent slept, half of the remaining attendees heard one-third and the other half heard two-thirds. What is the average number of minutes heard by the audience?

6) Suppose forty percent of the attendees listened to the entire talk, ten percent slept, half of the remaining attendees heard one-third and the other half heard two-thirds. What is the average number of minutes heard by the audience?

7) Suppose p percent listen to the entire talk, ten percent slept, half of the remaining attendees heard one-third of the talk and the other half heard two-thirds of the talk. Explain.

Explanation / Answer

(1) Avg time time listened = ( 20%*60+10%*0+35%*20+35%*40) =33 minutes

(2)Avg time time listened = ( 20%*60+10%*0+35%*15+35%*45) =33 minutes

(3)Avg time time listened = ( 20%*60+10%*0+35%*12+35%*48) =33 minutes

(4) As no of people same in both the groups sum of the time listened by is 60 min. Avg time will be equal to arthimetic mean of the times listened. Which will be equal to 30 min on avg on 70% of people which will be equal to 21 min. So total time will 33 min for all the cases.

(5)Avg time time listened = ( 30%*60+10%*0+30%*20+30%*40) =36 minutes

(6)Avg time time listened = ( 40%*60+10%*0+25%*15+25%*45) =39 minutes

(7)Avg time listened = (p%* 60+10%*0+(1-p)*30)

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