The average age of 160 boys in a class is 15 years. The average age of a group of 30 boys in the class is 16 years and the average age of another 50 boys in the class is 14 years. What is the average age of the remaining boys in the class?
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$15.25$
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$15.50$
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$15$
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$16.25$
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$None of these$
A
Correct answer
Explanation
Total age of all 160 boys = 160 × 15 = 2400 years. Sum of ages for first 30 boys = 30 × 16 = 480 years. Sum for next 50 boys = 50 × 14 = 700 years. Remaining boys = 160 - 30 - 50 = 80 boys with total age = 2400 - 1180 = 1220 years. Their average = 1220/80 = 15.25 years. This uses the weighted average principle.