The average weight of 12 students in a class is ‘y’ kg. Two new students joined them with total weight of 72 kg and the average weight of the class is decreased by $\frac{y}{16}$ kg. If the weight of heavier student out of two students who joined is $y-24$ kg, then find the difference between weight of two students who joined.

The correct answer is 8 kg.

We are given the following information:

- Original number of students = 12, with average weight = $y$ kg
- So total weight of 12 students = $12y$ kg
- Two new students joined with a combined weight of 72 kg
- After joining, total students = 14
- The new average decreased by $\frac{y}{16}$ kg, so new average = $y-\frac{y}{16}$ kg
- Weight of the heavier of the two new students = $y-24$ kg

Step 1: Set up the equation for the new average.

The new total weight is $12y+72$, and there are now 14 students. So:

$\frac{12y+72}{14}=y-\frac{y}{16}$

Step 2: Simplify the right-hand side.

$y-\frac{y}{16}=\frac{16}{y}-\frac{y}{16}=\frac{15}{y}$

More carefully:

$y-\frac{y}{16}=\frac{16}{y}=$

$\frac{16y-y}{16}=\frac{15}{y}$

So: $\frac{15y}{16}$

Step 3: Solve for y.

$\frac{12y+72}{14}=\frac{15y}{16}$

Cross-multiply:

$16(12y+72)=14\times 15y$

$192y+1152=210y$

$1152=210y-192y$

$1152=18y$

$y=\frac{1152}{18}=64$

So $y=64$ kg.

Step 4: Find the weights of the two new students.

- Weight of the heavier student = $y-24=64-24=40$ kg
- Combined weight of both = 72 kg
- Weight of the lighter student = $72-40=32$ kg

Step 5: Find the difference.

$40-32=8$ kg

The difference between the weights of the two students who joined is 8 kg.