The total number of students in class A and B is 92. The number of students in A is 30% more than that in B. The average weight (in kg) of students in B is 50% more than that of students in A. If the average weight of all the students in A and B is 56 kg, then what is the average weight (in kg) of students in B?

Let the number of students in class B be $$n_B$$. The number of students in class A is 30 % more than that in B, so

$$n_A = n_B + 0.30\,n_B = 1.3\,n_B$$

The total strength of the two classes is 92:

$$n_A + n_B = 92$$

Substituting $$n_A = 1.3\,n_B$$ gives

$$1.3\,n_B + n_B = 92 \;\Longrightarrow\; 2.3\,n_B = 92$$

$$n_B = \frac{92}{2.3} = 40$$

Therefore, $$n_A = 1.3 \times 40 = 52$$

Let the average weight of students in class A be $$x\,$$kg. The average weight of students in class B is 50 % more than that of A, so

$$\text{average of B} = 1.5\,x$$

The overall average weight of all 92 students is 56 kg. Using the formula for a weighted average,

$$\frac{n_A \times x \;+\; n_B \times (1.5\,x)}{n_A + n_B} = 56$$

Substitute $$n_A = 52$$ and $$n_B = 40$$:

$$\frac{52x + 40 \times 1.5x}{92} = 56$$

$$\frac{52x + 60x}{92} = 56$$

$$\frac{112x}{92} = 56$$

$$x = 56 \times \frac{92}{112} = 56 \times \frac{23}{28} = 2 \times 23 = 46$$

Thus, the average weight of class A is 46 kg. Hence, the average weight of class B is

$$1.5 \times 46 = 69 \text{ kg}$$

Option C which is: 69