If n=number of students in the original group, and S=the total weight of the group, then when A joins the group, the total weight is S+43 and the number in the group is n+1; when B joins the group along with A, the total weight becomes S+43+72=S+115, and there are n+2 students altogether.
The average weight when only A has joined the group is 61=(S+43)/(n+1); and the average weight when both have joined is 62=(S+115)/(n+2). We can rewrite these equations:
61(n+1)=S+43 and 62(n+2)=S+115,
61n+61=S+43 and 62n+124=S+115,
S=61n+61-43=61n+18 and S=62n+124-115=62n+9.
Therefore S=61n+18=62n+9, and if we take the last two expressions:
The average weight in the initial group is 567/9=63kg.