34. Vova is as many times older than his sister Galya as he is younger than his grandmother Katya. How old is each of them, if Galya is not yet 6 years old, and Vova together with his grandmother is already 112 years old?
34. Let Vova be $x$ times older than Gala. If Gala is 5 years old, then Vova is $5 x$, and Grandma Katya is $5 x \cdot x=5 x^{2}$. According to the condition, it should be $5 x+5 x^{2}=112$. But this is impossible, since 112 is not divisible by 5. Gala cannot be 3 years old either, since 112 is not divisible by 3. She cannot be 4 years old either, since $4 x+4 x^{2}=112$, which simplifies to $x(x+1)=38$, and 38 is not the product of two consecutive numbers. If Gala is 2 years old, then $2 x+2 x^{2}=112$, which simplifies to $x(x+1)=56$. The equation holds true when $x=7$. Therefore, Gala is 2 years old, Vova is 14 years old $(2 \cdot 7=14)$, and Grandma Katya is 98 years old $(14 \cdot 7=98)$. (Wish Grandma good health!)