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The average age of 80 boys in a class is 15 years. The average age of a group of 15 boys in the class is 16 years and the average age of another 25 boys in the class is 14 years. What is the average age of the remaining boys in the class?
- a)15.25 years
- b)14 years
- c)14.75 years
- d)Cannot be determined
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Given Data
- Total number of boys in the class: 80
- Average age of all boys: 15 years
- Average age of 15 boys: 16 years
- Average age of 25 boys: 14 years
Total Age Calculation
- Total age of all boys = Average age × Total number of boys
- Total age of all boys = 15 years × 80 = 1200 years
Age of Group 1
- Total age of 15 boys = Average age × Number of boys
- Total age of 15 boys = 16 years × 15 = 240 years
Age of Group 2
- Total age of 25 boys = Average age × Number of boys
- Total age of 25 boys = 14 years × 25 = 350 years
Combined Age of Groups
- Total age of the two groups = Age of Group 1 + Age of Group 2
- Total age of the two groups = 240 years + 350 years = 590 years
Remaining Age Calculation
- Total age of remaining boys = Total age of all boys - Total age of the two groups
- Total age of remaining boys = 1200 years - 590 years = 610 years
Number of Remaining Boys
- Total remaining boys = Total boys - (Group 1 boys + Group 2 boys)
- Total remaining boys = 80 - (15 + 25) = 40 boys
Average Age of Remaining Boys
- Average age of remaining boys = Total age of remaining boys / Number of remaining boys
- Average age of remaining boys = 610 years / 40 boys = 15.25 years
Conclusion
- The average age of the remaining boys in the class is 15.25 years. Thus, the correct answer is option 'A'.
- Total number of boys in the class: 80
- Average age of all boys: 15 years
- Average age of 15 boys: 16 years
- Average age of 25 boys: 14 years
Total Age Calculation
- Total age of all boys = Average age × Total number of boys
- Total age of all boys = 15 years × 80 = 1200 years
Age of Group 1
- Total age of 15 boys = Average age × Number of boys
- Total age of 15 boys = 16 years × 15 = 240 years
Age of Group 2
- Total age of 25 boys = Average age × Number of boys
- Total age of 25 boys = 14 years × 25 = 350 years
Combined Age of Groups
- Total age of the two groups = Age of Group 1 + Age of Group 2
- Total age of the two groups = 240 years + 350 years = 590 years
Remaining Age Calculation
- Total age of remaining boys = Total age of all boys - Total age of the two groups
- Total age of remaining boys = 1200 years - 590 years = 610 years
Number of Remaining Boys
- Total remaining boys = Total boys - (Group 1 boys + Group 2 boys)
- Total remaining boys = 80 - (15 + 25) = 40 boys
Average Age of Remaining Boys
- Average age of remaining boys = Total age of remaining boys / Number of remaining boys
- Average age of remaining boys = 610 years / 40 boys = 15.25 years
Conclusion
- The average age of the remaining boys in the class is 15.25 years. Thus, the correct answer is option 'A'.
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The average age of 80 boys in a class is 15 years. The average age of a group of 15 boys in the class is 16 years and the average age of another 25 boys in the class is 14 years. What is the average age of the remaining boys in the class?a)15.25 yearsb)14 yearsc)14.75 yearsd)Cannot be determinede)None of theseCorrect answer is option 'A'. Can you explain this answer?
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