The total number of students in class A and B is 96. The number of students in A is 40% more than that in B. The average weight (in kg) of the students in B is 50% more than that of the students in A. If the average weight of all the students in A and B taken together is 58 kg, then what is the average weight of the students in B?

Given that,
total number number of student in class A and B=96
Let total number of student in B=X

As per the condition, the number of student in the class A $$=X+\dfrac{40\times X}{100}= \dfrac{7X} {5}$$
Hence, $$\dfrac{7X}{5}+X=96$$
$$12X=96\times 5$$
$$X=40$$

So number of student class B=40

Number of student in class A$$=\dfrac{7X}{5}=\dfrac{7\times 40}{5}=56$$
Let the average weight of the class A be W

then, average weight of class B$$=W+\dfrac{W\times 50}{100}=\dfrac{3W}{2}$$

Now, $$\dfrac{\dfrac{3W\times 40}{2}+56\times W}{96}=58$$
$$\dfrac{116W}{96}=58$$
$$W=\dfrac{58\times 96}{116}$$

$$W=48$$
Hence, the average weight of class B $$ \dfrac{3W}{2}=\dfrac{3\times 48}{2}=72kg$$