In class 6T, when only one girl stands up and the rest of the children are sitting down, the number of boys sitting down is $\tfrac{1}{2}$ the number of girls sitting down. When only one boy stands up and the rest of the children are sitting down, the ratio of the number of girls sitting down to the number of boys sitting down is $3 : 4$.

1. (a)

   What is the total number of children in class 6T?

2. (b)

   After an equal number of girls and boys left the class for a competition, the ratio of the number of girls to the number of boys left in the class became $3 : 2$. Find the total number of children who left the class for the competition.