SWATI ROW A BOAT IN A …

Let the speed of the stream be x km/hr.
 Speed of boat upstream = (5 - x) km/hr.
Speed of boat downstream = (5 + x) km/hr.
Time taken to go upstream = {tex} \frac { 5.25 } { 5 - x }{/tex} hours.
Time taken to go downstream = {tex} \frac { 5.25 } { 5 + x }{/tex} hours.

According to question,
{tex} \therefore \quad \frac { 5.25 } { 5 - x } - \frac { 5.25 } { 5 + x } = 1{/tex}
{tex} \Rightarrow \quad 5.25 [ \frac { 1 } { 5 - x } - \frac { 1 } { 5 + x } ] = 1{/tex}
{tex} \Rightarrow \quad \frac { 21 } { 4 } [ \frac { 5 + x - 5 + x } { ( 5 - x ) ( 5 + x ) } ] = 1{/tex}
{tex} \Rightarrow \quad \frac { 21 } { 4 } \times \frac { 2 x } { 25 - x ^ { 2 } } = 1{/tex}
{tex} \Rightarrow \quad 21 x = 50 - 2 x ^ { 2 }{/tex}
{tex} \Rightarrow{/tex} 2x² + 21x - 50 = 0
{tex}\Rightarrow{/tex} 2x² + 25x - 4x - 50 = 0
{tex} \Rightarrow \quad x ( 2 x + 25 ) - 2 ( 2 x + 25 ) = 0{/tex}
{tex} \Rightarrow{/tex} (2x + 25) (x - 2) = 0
{tex} \Rightarrow{/tex} x - 2 = 0, 2x + 25 = 0

 {tex} \Rightarrow{/tex} x = 2 {tex} \left[ \because x \neq - \frac { 25 } { 2 } \text { as } x > 0 \right]{/tex}
Hence, the speed of the stream is 2 km/hr.