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SWATI ROW A BOAT IN A STILL WATER AT SPEED OF 5 KM/HR |
| Answer» Let the speed of the stream be x km/hr.\xa0Speed of\xa0boat upstream = (5 - x) km/hr.Speed of\xa0boat downstream = (5 + x) km/hr.Time taken to\xa0go\xa0upstream = {tex} \\frac { 5.25 } { 5 - x }{/tex}\xa0hours.Time taken to go\xa0downstream = {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}\xa02x2 + 21x - 50 = 0{tex}\\Rightarrow{/tex}\xa02x2 + 25x - 4x - 50 = 0{tex} \\Rightarrow \\quad x ( 2 x + 25 ) - 2 ( 2 x + 25 ) = 0{/tex}{tex} \\Rightarrow{/tex}\xa0(2x + 25) (x - 2) = 0{tex} \\Rightarrow{/tex}\xa0x - 2 = 0, 2x + 25 = 0\xa0{tex} \\Rightarrow{/tex}\xa0x = 2\xa0{tex} \\left[ \\because x \\neq - \\frac { 25 } { 2 } \\text { as } x > 0 \\right]{/tex}Hence, the speed of the stream is 2 km/hr. | |