The mean age of 33 students of a class is 13 years. If one girl leaves the class, the mean becomes $12\dfrac{15}{16}$ years. What is the age of the girl ?

$\text{Arithmetic mean (A.M.)} = \dfrac{\text{Sum of age of students}}{\text{No.of students}} \\[1em] \Rightarrow 13 = \dfrac{\text{Sum of age of students}}{33} \\[1em] \Rightarrow \text{Sum of age of students} = 33 \times 13 \\[1em] \Rightarrow \text{Sum of age of students} = 429.$

Let the age of girl that leaves the class be x. So, sum of age of students becomes 429 - x and total no of students = 32. Given, new mean = $12\dfrac{15}{16}$.

$\therefore 12\dfrac{15}{16} = \dfrac{429 - x}{32} \\[1em] \dfrac{207}{16} = \dfrac{429 -x}{32} \\[1em] 207 \times 32 = 16(429 - x) \\[1em] 6624 = 6864 - 16x \\[1em] 16x = 6864 - 6624 \\[1em] 16x = 240 \\[1em] x = \dfrac{240}{16} = 15.$

Hence, the age of girl is 15 years.