Question 74

A boat goes 24 km upstream and 28 km dowstream in 6 hours. If it goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes, find the speed of the stream.


Let speed of boat = $$x$$ km/hr and speed of stream = $$y$$ km/hr

=> Downstream speed = $$(x+y)$$ km/hr and downstream speed = $$(x-y)$$ km/hr

According to ques,

=> $$\frac{24}{x-y}+\frac{28}{x+y}=6$$ ----------(i)

and $$\frac{30}{x-y}+\frac{21}{x+y}=6.5$$ -------(ii)

Using the operation : 4 x (ii)-3 x (i)

=> $$\frac{48}{x-y}=26-18$$

=> $$x-y=\frac{48}{8}=6$$ --------(iii)

Similarly, $$x+y=14$$ -------------(iv)

Now, subtracting equation (iii) from (iv), => $$2y=8$$

=> $$y=\frac{8}{2}=4$$

$$\therefore$$ Speed of stream = 4 km/hr

=> Ans - (C)

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