Multiple choice

A speaker talked for sixty minutes to a full auditorium. Ten percent of the audience listened to the entire talk, and twenty percent slept through the entire talk. Half of the remaining listened to one-third of the talk, and the other half listened to two-thirds of the talk. Find out the average number of minutes for which the audience listened to the talk.

  1. 25

  2. 26

  3. 27

  4. 31
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

10% listened for 60 min. 20% listened for 0 min. Remaining 70%: half (35%) listened for 1/3 of 60 = 20 min, half (35%) listened for 2/3 of 60 = 40 min. Average = (0.1*60 + 0.2*0 + 0.35*20 + 0.35*40) = 6 + 0 + 7 + 14 = 27.

AI explanation

Assume the total audience size is 100 people. The first 10 people listened for 60 minutes each, totaling 600 minutes, and the next 20 people listened for 0 minutes. The remaining audience is 70 people, so 35 people listened for one-third of the talk (20 minutes) and the other 35 listened for two-thirds of the talk (40 minutes). The total minutes listened by these 70 people is (35 times 20) plus (35 times 40), which equals 2100 minutes. Adding the 600 minutes from the first group gives a grand total of 2700 minutes, and dividing this by the 100 total people gives an average of 27 minutes.

Keep practicing — related questions