WAEC Mathematics 2017 Paper

Concept:Average is the total sum divided by the number of items. When a new member joins, add her age to the old total and divide by the new number of members.Explanation:Convert 12 years 4 months into years.Since 12 months = 1 year, 4 months = $\frac{4}{12} = \frac{1}{3}$ year.So the joining girl's age is $12 + \frac{1}{3} = \frac{37}{3}$ years.Find the total age of the 25 girls.Average = 10 years, so total age = $25 \times 10 = 250$ years.Add the new girl's age to get the new total.New total = $250 + \frac{37}{3} = \frac{750}{3} + \frac{37}{3} = \frac{787}{3}$ years.The new number of girls is $25 + 1 = 26$.New average = $\frac{\frac{787}{3}}{26} = \frac{787}{78} = 10.0897... \approx 10.1$ years.Answer:The new average age is 10.1 years, so the correct option is A.