Let Hema's age be $x,$ Hari's age be $y$ and Suresh's age be $z.$
According to the question:
- $x=5+2y\implies x-2y=5\qquad \to (1)$
- $z=10y-13\qquad \to (2)$
- $z=3x\qquad \to(3)$
From $(2)$ and $(3)$ we get
- $3x-10y=-13\qquad \to(4)$
Solving equations $(1), \ (4)$ and $(3)$ we get $x=19,\ y=7$ and $z=57.$
Hema's age, $x=19$
So, the correct answer is $(D).$