A man can row three-quarters of a kilometre against the stream in 11¹/₄ minutes and down the stream in 7¹/₂ minutes. The speed (in km/hr) of the man in still water is:

Explanation:-

$$\eqalign{ & {\text{We}}\,{\text{can}}\,{\text{write}}\,{\text{three - quarters}}\,{\text{of}}\,{\text{akilometre}}\,{\text{as750}}\,{\text{metres}}. \cr & {\text{and}}\,11\frac{1}{4}\,{\text{minutes}}\,{\text{as}}\,{\text{675}}\,{\text{seconds}}{\text{.}} \cr & {\text{Rate}}\,{\text{upstream}} \cr & = \left( {\frac{{750}}{{675}}} \right)m/\sec = \frac{{10}}{9}m/\sec \cr & {\text{Rate}}\,{\text{downstream}} \cr & = \left( {\frac{{750}}{{450}}} \right)m/\sec = \frac{5}{3}m/\sec \cr & \therefore {\text{Rate}}\,{\text{in}}\,{\text{still}}\,{\text{water}} \cr & = \frac{1}{2}\left( {\frac{{10}}{9} + \frac{5}{3}} \right)m/\sec \cr & = \frac{{25}}{{18}}\,m/\sec \cr & = \left( {\frac{{25}}{{18}} \times \frac{{18}}{5}} \right)km/hr \cr & = 5\,km/hr \cr}$$