Explanation:
\(10 = \frac{L}{v}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
\(12.5 = \frac{L}{{\sqrt {{v^2} - {u^2}} }} = \frac{L}{{v\sqrt {1 - {u^2}/{v^2}} }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
From (1) and (2) \(\frac{{10}}{{12.5}} = \frac{L}{v} \times \frac{{v\sqrt {1 - {u^2}/{v^2}} }}{L}\)
\(\frac{4}{5} = \sqrt {1 - \frac{{{{12}^2}}}{{{v^2}}}} \)
\(\frac{{16}}{{25}} = 1 - \frac{{{{12}^2}}}{{{v^2}}} \Rightarrow \frac{{{{12}^2}}}{{{v^2}}} = 1 - \frac{{16}}{{25}} = \frac{9}{{25}}\)
\(\frac{{12}}{v} = \frac{3}{5}\; \Rightarrow \;v = \frac{{12 \times 5}}{3} = 20\,m/s\)