The average weight of 12 students in a class is $y$ kg. Two new students join the class with a combined weight of $72$ kg, and as a result, the average weight of the class decreases by $\frac{y}{16}$ kg. If the heavier student among the two new students weighs $y - 24$ kg, what is the difference between the weights of the two new students?

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**Solution:**

1. Let the average weight of the original 12 students be $y$ kg.

2. Total weight of the original 12 students = $12y$.

3. Two new students join with a combined weight of $72$ kg.

4. New total number of students = $12 + 2 = 14$.

5. New average weight = original average minus $\frac{y}{16}$:
   $$	ext{New average} = y - \frac{y}{16} = \frac{15y}{16}$$

6. Total weight of all 14 students after new students join:
   $$14 	imes \frac{15y}{16} = \frac{210y}{16} = \frac{105y}{8}$$

7. Total weight of all students after new students join is also:
   $$12y + 72$$

8. Equate the two expressions for total weight:
   $$12y + 72 = \frac{105y}{8}$$

9. Multiply both sides by 8 to clear denominator:
   $$96y + 576 = 105y$$

10. Rearranging:
    $$105y - 96y = 576$$
    $$9y = 576$$
    $$y = \frac{576}{9} = 64$$

11. Weight of heavier student = $y - 24 = 64 - 24 = 40$ kg.

12. Let the weight of the lighter student be $x$ kg.

13. Since combined weight of two new students is 72 kg:
    $$x + 40 = 72 \implies x = 32$$

14. Difference between weights:
    $$40 - 32 = 8 	ext{ kg}$$

**Answer:** 8 kg

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