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The average weight of 8 persons increases by 2.5 kg when one person whose weight is 65 kg is replaced by a new person. What Is the weight of the new person?
- a)78 kg
- b)82 kg
- c)85 kg
- d)80 kg
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The average weight of 8 persons increases by 2.5 kg when one person w...
Total increase in weight due to addition of new persons = 2.5 × 8 = 20 kg
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Weight of new person = 65 + 20 = 85 kg
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The average weight of 8 persons increases by 2.5 kg when one person w...
Understanding the Problem
When a person weighing 65 kg is replaced by a new person, the average weight of the group of 8 people increases by 2.5 kg.
Calculating the Initial Average Weight
- Let the initial average weight of the 8 persons be X kg.
- Therefore, total initial weight = 8 * X kg.
Effect of Replacement on Average Weight
- When the person weighing 65 kg is replaced, the new average becomes (X + 2.5) kg.
- The new total weight = 8 * (X + 2.5) kg.
Setting Up the Equation
- The weight of the new person can be found using the equation:
- Total weight after replacement = Total weight before replacement - Weight of replaced person + Weight of new person.
- This translates to:
- 8 * (X + 2.5) = 8 * X - 65 + Weight of new person.
Simplifying the Equation
- Expanding both sides:
- 8X + 20 = 8X - 65 + Weight of new person.
- As 8X cancels out:
- 20 + 65 = Weight of new person.
- Weight of new person = 85 kg.
Conclusion
Thus, the weight of the new person is 85 kg, matching option 'C'.
When a person weighing 65 kg is replaced by a new person, the average weight of the group of 8 people increases by 2.5 kg.
Calculating the Initial Average Weight
- Let the initial average weight of the 8 persons be X kg.
- Therefore, total initial weight = 8 * X kg.
Effect of Replacement on Average Weight
- When the person weighing 65 kg is replaced, the new average becomes (X + 2.5) kg.
- The new total weight = 8 * (X + 2.5) kg.
Setting Up the Equation
- The weight of the new person can be found using the equation:
- Total weight after replacement = Total weight before replacement - Weight of replaced person + Weight of new person.
- This translates to:
- 8 * (X + 2.5) = 8 * X - 65 + Weight of new person.
Simplifying the Equation
- Expanding both sides:
- 8X + 20 = 8X - 65 + Weight of new person.
- As 8X cancels out:
- 20 + 65 = Weight of new person.
- Weight of new person = 85 kg.
Conclusion
Thus, the weight of the new person is 85 kg, matching option 'C'.
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The average weight of 8 persons increases by 2.5 kg when one person whose weight is 65 kg is replaced by a new person. What Is the weight of the new person?a)78 kgb)82 kgc)85 kgd)80 kgCorrect answer is option 'C'. Can you explain this answer?
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