The mean age of n men in a club is 50 years. Two men aged 55 and 63 years left the club, and the mean age reduced by 1 year. Find the value of n.
Let the sum of the men's ages be f, so that
\(\frac{f}{n} = 50 .... (1)\)
Also, \(\frac{f - (55 + 63)}{n - 2} = 50 - 1 = 49 .... (2)\)
From (1), \(f = 50n\)
From (2), \(f - 118 = 49(n - 2) = 49n - 98\)
\(f = 49n - 98 + 118 = 49n + 20\)
\(\therefore f = 50n = 49n + 20\)
\(50n - 49n = n = 20\)
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