Time constant for series combination \(=\frac{R C}{2}\)

In first case :

\(V=V_{0} e^{\frac{t_{1}}{2 R C}}=\frac{V_{0}}{2}\)

In second case :

\(V=V_{0} e^{\frac{t_{2}}{(R C / 2)}}=\frac{V_{0}}{2}\)

\(\frac{t_{1}}{2 R C}=\frac{t_{2}}{(R C / 2)}\)

\(\Rightarrow \quad t_{2}=\frac{t_{1}}{4}=\frac{10}{4}=2.5\; sec\)