Question
The average age of a group of 70 students is 13 years.
If 3 students whose ages are 15 years, 21 years, and _____ years are replaced by 3 new students whose ages are _____ years, 19 years, and 29 years, then the new average age of the group increases by 0.35 years. The values given in which of the following options will fill the blanks in the same order to make the above statement true: I. 27, 38 II. 33, 44 III. 20, 30Solution
Since the new average increases by 0.35 years, the difference in the sum of ages of the students who left and the new students should be: 70×0.35=24.5 years Option I: (38+19+29)−(15+21+27)=23 years So, option I cannot be the answer. Option II: (44+19+29)−(15+21+33)=23 years So, option II cannot be the answer. Option III: (30+19+29)−(15+21+20)=22 years So, option III cannot be the answer.
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