Given: Average height of class initially = 152 cm Average height of class when 2 new students join = 154 cm Number of students in class = 13 Heights of students who left the school = (161 cm, 133 cm) Ratio of heights of new students = 2 : 3 Formula Used: Average Height = Sum of heights/Total number of students Calculations: Let the total sum of heights of students be s. Let the sum of heights of students who are in the school permanently be s’. Let the heights of new students be h and H respectively. Sum of heights of all the students = s = 152 × 13 ⇒ s = 1976 cm Sum of heights of students who left the school = (161 + 133) cm ⇒ Sum of heights of students who left the school = 294 cm When 2 old students left the school, s = s’ + 294 ⇒ 1976 cm = s’ + 294 cm ⇒ s’ = 1682 cm When 2 new students join the school, Average height = 154 cm ⇒ Sum of heights of all the students = 154 × 13 = 2002 cm 2002 cm = s’ + (h + H) ⇒ 2002 cm = 1682 cm + (h + H) ⇒ (h + H) = 320 h : H = 2 : 3 1 unit = 320/(2 + 3) = 64 ⇒ h = 2 × 64 cm = 128 cm ⇒ H = 3 × 64 cm = 192 cm ∴ The heights of the new students are 128 cm and 192 cm respectively.