Quantitative Aptitude Ques 1299

Question: In a stream running at 5 km/h, a motorboat goes 1 km upstream and back again to the starting point in 35 min. Find the speed of the motorboat in still water.

Options:

A) 12 km/h

B) 5 km/h

C) 7 km/h

D) 14 km/h

Show Answer

Answer:

Correct Answer: C

Solution:

  • Let the speed of the motorboat in still water be x km/h. Downstream speed $ =(x+5)km/h $ Upstream speed $ =(x-5)km/h $

$ \therefore $ $ \frac{1}{x+5}+\frac{1}{x-5}=\frac{35}{60} $

$ \Rightarrow $ $ \frac{2x}{x^{2}-25}=\frac{7}{12} $

$ \Rightarrow $ $ 7(x^{2}-25)=24x $

$ \Rightarrow $ $ 7x^{2}-24x-175=0 $

$ \Rightarrow $ $ 7x(x-7)+24(x-7)=0 $

$ \Rightarrow $ $ (x-7)(7x+24)=0 $ $ x=7 $ Thus, speed of the motorboat in still water $ =7km/h $

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