WAEC Mathematics 2010 Paper

Concept:The mean age is the total sum of ages divided by the number of men. Use the given change in mean to form an equation and solve for $R$.Explanation:Let the sum of ages of all $R$ men be $S$.Original mean age is $50$ years.So, $\frac{S}{R} = 50$, which gives $S = 50R$.The two men who left are aged $55$ and $63$.Their total age is $55 + 63 = 118$.Remaining sum of ages is $50R - 118$.Remaining number of men is $R - 2$.The mean age reduced by $1$ year, so the new mean is $50 - 1 = 49$ years.Thus, $\frac{50R - 118}{R - 2} = 49$.Multiply both sides by $R - 2$: $50R - 118 = 49(R - 2)$.Expand: $50R - 118 = 49R - 98$.Bring like terms together: $50R - 49R = -98 + 118$.So, $R = 20$.Answer:$R = 20$, which is option B.