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The average age of 25 men is decreased by 1 1/2 years when one of them wh is 60 years is replaced by a new man. What is the age of the new man?
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The average age of 25 men is decreased by 1 1/2 years when one of them...
Given Data:
- The average age of 25 men is decreased by 1 1/2 years when one of them who is 60 years is replaced by a new man.
To Find:
- The age of the new man.
Solution:
- Let the sum of the ages of the 25 men be S.
- The average age of the 25 men = S/25.
- When one of the men who is 60 years is replaced by a new man, the sum of ages remains the same but the average decreases by 1 1/2 years.
Step 1: Calculate the Initial Average Age:
- Initial average age = S/25
- Sum of ages initially = 25 * (S/25) = S
Step 2: Calculate the Final Average Age:
- Final average age = (S - 60 + x)/25, where x is the age of the new man.
Step 3: Formulate the Equation:
- According to the given data, the final average age is 1 1/2 years less than the initial average age.
- So, (S/25) - 3/2 = (S - 60 + x)/25
Step 4: Solve for x:
- (S/25) - 3/2 = (S - 60 + x)/25
- (S - 3S/2) = S - 60 + x
- S/2 = 60 + x
- x = S/2 - 60
Step 5: Substitute the Initial Average Age into the Equation:
- x = S/2 - 60
- x = S/2 - 60
- x = (2 * S - 120)/2
- x = S - 60
Therefore, the age of the new man is 60 years.
- The average age of 25 men is decreased by 1 1/2 years when one of them who is 60 years is replaced by a new man.
To Find:
- The age of the new man.
Solution:
- Let the sum of the ages of the 25 men be S.
- The average age of the 25 men = S/25.
- When one of the men who is 60 years is replaced by a new man, the sum of ages remains the same but the average decreases by 1 1/2 years.
Step 1: Calculate the Initial Average Age:
- Initial average age = S/25
- Sum of ages initially = 25 * (S/25) = S
Step 2: Calculate the Final Average Age:
- Final average age = (S - 60 + x)/25, where x is the age of the new man.
Step 3: Formulate the Equation:
- According to the given data, the final average age is 1 1/2 years less than the initial average age.
- So, (S/25) - 3/2 = (S - 60 + x)/25
Step 4: Solve for x:
- (S/25) - 3/2 = (S - 60 + x)/25
- (S - 3S/2) = S - 60 + x
- S/2 = 60 + x
- x = S/2 - 60
Step 5: Substitute the Initial Average Age into the Equation:
- x = S/2 - 60
- x = S/2 - 60
- x = (2 * S - 120)/2
- x = S - 60
Therefore, the age of the new man is 60 years.
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The average age of 25 men is decreased by 1 1/2 years when one of them wh is 60 years is replaced by a new man. What is the age of the new man?
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The average age of 25 men is decreased by 1 1/2 years when one of them wh is 60 years is replaced by a new man. What is the age of the new man? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about The average age of 25 men is decreased by 1 1/2 years when one of them wh is 60 years is replaced by a new man. What is the age of the new man? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average age of 25 men is decreased by 1 1/2 years when one of them wh is 60 years is replaced by a new man. What is the age of the new man?.
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