Question 138

# A man rows to a place 35 km in distant and back in 10 hours 30 minutes. He found that he could row 5 km with the flow of stream in the same time as he can row 4 km against the stream. Find the rate of flow of the stream.

Solution

Let speed of man in still water = $$x$$ km/hr and speed of stream = $$y$$ km/hr

Speed downstream =Â $$(x+y)$$ km/hr and speed upstream =Â $$(x-y)$$ km/hr

TheÂ man can row 35 km to and back in 10 hours 30 minutes.

Using, time = distance/speed

=> $$\frac{35}{x+y}+\frac{35}{x-y}=10.5$$

=> $$\frac{1}{x+y}+\frac{1}{x-y}=\frac{10.5}{35}$$

=> $$\frac{1}{x+y}+\frac{1}{x-y}=0.3$$ -------------(i)

Also, $$\frac{5}{x+y}=\frac{4}{x-y}$$

=> $$5x-5y=4x+4y$$

=> $$5x-4x=4y+5y$$

=> $$x=9y$$ -------------(ii)

Substituting above value in equation (i), we getÂ :

=>Â $$\frac{1}{9y+y}+\frac{1}{9y-y}=0.3$$

=>Â $$\frac{1}{10y}+\frac{1}{8y}=0.3$$

=> $$\frac{10+8}{80}=0.3y$$

=> $$0.3y\times80=18$$

=> $$y=\frac{18}{24}=0.75$$

$$\therefore$$ Rate of flow of the stream =Â 0.75 km/hr

=> Ans - (C)

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