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10 Aug 2024, 23:45
Kudos
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C
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Difficulty:
25%
(medium)
Question Stats:
87% (02:35) correct
13%
(02:38)
wrong
based on 31
sessions
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Not Attempted Yet
In a class of 11 students, the average age of all the students is m years. If one student left the class, now the difference between the maximum possible average to the minimum possible average age of the class is 4. What is the difference in the age of the eldest member and the youngest member of the initial class?
A. 30
B. 35
C. 40
D. 45
E. 50
A. 30
B. 35
C. 40
D. 45
E. 50
11 Aug 2024, 00:00
Kudos
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Bunuel
Let's assume
- The maximum weight in the group is represented by \(W_{\text{max}}\)
- The minimum weight in the group is represented by \(W_{\text{min}}\)
- Max Average = \(A_{\text{max}}\)
- Min Average = \(A_{\text{min}}\)
Given:
\(A_{\text{max}} - A_{\text{min}} = 4\)
We can deduce that, when the student with maximum weight leaves the group, the new average is minimum. Hence,
\(11m - W_{\text{max}} = 10*A_{\text{min}}\) ---- (1)
Similarly, when the student with the minimum weight leaves the group, the new average is the maximum.
\(11m - W_{\text{min}} = 10*A_{\text{max}}\) --- (2)
(2) - (1)
\(10(A_{\text{max}} - A_{\text{min}}) = W_{\text{max}} - W_{\text{min}}\)
\(W_{\text{max}} - W_{\text{min}} = 10 * 4 = 40\)
Option C
