The average age of 8 persons in a committee is increased by two years ...
Let the average age of the women be A years.
Total of their ages = 2A
Total of the eight persons = ET
When replaced (ET - 80 + 2A)/8 = ET/8 + 2
2A - 80 = 16
A = 96/2 = 48
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The average age of 8 persons in a committee is increased by two years ...
Given Information:
- Average age of 8 persons in the committee increases by 2 years when two men aged 35 and 45 are replaced by two women.
Calculating the Initial Average Age:
- Let the initial sum of ages of 8 persons be x.
- Initial average age = x/8
Calculating the Final Average Age:
- After replacing two men with two women, the new sum of ages will be x - 35 - 45 + 2w + 2w, where w is the average age of the two women.
- Final average age = (x - 35 - 45 + 2w + 2w)/8
Using the Given Information:
- From the given information, we know that the final average age is 2 years higher than the initial average age.
- Therefore, we can set up the equation: (x - 35 - 45 + 2w + 2w)/8 = x/8 + 2
Solving the Equation:
- Simplifying the equation, we get: (x - 80 + 4w) / 8 = x/8 + 2
- Further simplifying, we get: x - 80 + 4w = x + 16
- Rearranging the terms, we get: 4w = 96
- Therefore, the average age of the two women is 96/2 = 48 years.
Therefore, the average age of the two women is 48 years. Hence, the correct answer is option 'C'.