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.
Answer Details
Let's denote the sum of ages of the n men in the club by S. Then we know that:
Mean age of n men = S/n = 50
Multiplying both sides by n, we get:
S = 50n
After two men aged 55 and 63 years leave the club, the sum of ages of the remaining men becomes:
S' = S - 55 - 63 = 50n - 118
The new mean age is reduced by 1 year, so we have:
S'/(n-2) = 50 - 1
Simplifying this equation and substituting S', we get:
(50n - 118)/(n-2) = 49
Multiplying both sides by n-2, we get:
50n - 118 = 49(n-2)
Simplifying this equation, we get:
n = 20
Therefore, there were originally 20 men in the club.