3. A motor boat covers a certain di...
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3. A motor boat covers a certain distance down- stream in a river in 3 hours. It covers the same distance upstream in 3 hours and a half. If the speed of water is 1.5 km/h, then the speed of the boat in still water is : (1) 17 km/h (2) 19.5 km/h (3) 17.5 km/h (4) 19 km/h

11th - 12th Class
Maths
Solution
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Sol. (2) Let the speed of boat in still water be ( x ) kmph and the distance be ( y ) km. ( therefore quad ) Rate downstream ( =(x+1.5) mathrm{kmph} ) Rate upstream ( =(x-1.5) mathrm{kmph} ) According to the question, ( frac{y}{x+1.5}=3 ) ( frac{y}{x-1.5}=frac{7}{2} ) On dividing equation (i) by (ii), ( frac{x-1.5}{x+1.5}=frac{3 times 2}{7}=frac{6}{7} ) ( Rightarrow 7 x-10.5=6 x+9 ) ( Rightarrow x=10.5+9=19.5 mathrm{kmph} )
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