Speed of boat in still water = 5 km/hr

Let speed of the stream be a km/hr

⇒ Speed upstream = 5 - a

⇒ Speed downstream = 5 + a

Distance rowed = 10.5 km

Let the time taken to return downstream be ‘t’ hours

⇒ time taken to go upstream = t + 63/16 hours

Distance = Speed × time

⇒ 10.5 = (5 + a) × t          Downstream rowing

$(\Rightarrow {\rm{\;t\;}} = {\rm{\;}}\frac{{10.5}}{{5\; + \;a}})$      ----(1)         

⇒ 10.5 = (5 - a) × (t + 63/16)Upstream rowing     ----(2)

Substituting (1) in (2):

$(\begin{array}{l} 10.5 = \left( {5 - a} \right) \times \left( {\frac{{10.5}}{{5\; + \;a}}\; + \;\frac{{63}}{{16}}} \right)\\ \Rightarrow \frac{{21}}{2}\left[ {\frac{1}{{5 - a}} - \frac{1}{{5\; + \;a}}} \right]\; = \;\frac{{63}}{{16}} \end{array})$

$(\Rightarrow \frac{{2a}}{{25 - {a^2}}}\; = \;\frac{3}{8} \Rightarrow 3{a^2}\; + \;16a - 75\; = \;0)$

$(\left( {a - 3} \right)\left( {3a\; + \;25} \right)\; = \;0)$      (Splitting the middle term)

⇒ a = 3 or a= -25/3(Discarded because negative value)