(a) According to problem
Distance travelled by body $A$ in $5^{th}\ sec$ and distance travelled by body $B$ in $3^{rd}\ sec$. of its motion are equal.
$0 + \frac{a_{1}}{2}(2 \times 5 - 1) = 0 + \frac{a_{2}}{2}\lbrack 2 \times 3 - 1\rbrack$
$9a_{1} = 5a_{2} \Rightarrow \frac{a_{1}}{a_{2}} = \frac{5}{9}$