A boat takes 8 hr. to cover 65 km in upstream and 75 km in downstream. While it takes 7 hr. 36 min. to cover 52 km in upstream and 90 km in downstream. Then find the speed of boat in still water.

19 km/hr

Let the speed of boat = U km/h

Speed of stream = V km/hr

ATQ,   \(\frac{65}{U-V}\) + \(\frac{75}{U+V}\) = 8 -------- (i)

          \(\frac{52}{U-V}\) + \(\frac{90}{U+V}\) = 7\(\frac{3}{5}\) ----- (ii)

Note :- Take common factor for easy calculation

           (65  ,  52)          (75     ,     90)

             ⇓        ⇓              ⇓             ⇓

                  13                        25

So, U+V = 25 and U-V = 13 satisfy the equation

Then (U) speed of boat =  \(\frac{25+13}{2}\) = 19 km/hr