Question 147

A motor boat covers a certain distance downstream in a river in 3 hours. It covers the same distance upstream in 3 hours and half. If the speed of the water is 1.5 km/h, then the speed of the boat in still water is :

Solution

Let speed of boat = $$x$$ km/hr

=> Downstream speed = $$(x+1.5)$$ km and upstream speed = $$(x-1.5)$$ km

$$\because$$ Distance travelled is same and speed is inversely proportional to time,

=> $$\frac{x+1.5}{x-1.5}=\frac{3.5}{3}$$

=> $$3x+4.5=3.5x-5.25$$

=> $$3.5x-3x=4.5+5.25$$

=> $$\frac{x}{2}=9.75$$

=> $$x=9.75\times2=19.5$$

$$\therefore$$ Speed of the boat in still water = $$19.5$$ km/hr

=> Ans - (C)

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