jmc

Shea has grown $20\%$, if x was her original height, then $1.2x=60$, so she was originally $\frac{60}{1.2}=50$ inches tall which is a $60-50=10$ inch increase. Ara also started off at $50$ inches. Since Ara grew half as much as Shea, Ara grew $\frac{10}{2}=5$ inches. Therefore, Ara is now $50+5=55$ inches tall which is choice $\boxed{55}.$