SATHEE: Quantitative Aptitude Ques 1390

Quantitative Aptitude Ques 1390

Question: In a stream running at 2 km/h, a motorboat goes 5 km upstream and back again to the starting point in 1 h 20 min. Find the speed of the motorboat in still water.

Options:

A) 4 km/h

B) 8 km/h

C) 10 km/h

D) 6 km/h

Show Answer

Answer:

Correct Answer: B

Solution:

Let the speed of the motorboat in still water be $ x=km/h. $
Downstream speed $ =(x+2)km/h $ Upstream speed $ =(x-2)km/h $

$ \therefore $ $ \frac{5}{x+2}+\frac{5}{x-2}=\frac{4}{3} $

$ \Rightarrow $ $ \frac{1}{x+2}+\frac{1}{x-2}=\frac{4}{3} $

$ \Rightarrow $ $ \frac{2x}{x^{2}-4}=\frac{4}{15} $

$ \Rightarrow $ $ 4x^{2}-16=30x $

$ \Rightarrow $ $ 4x^{2}-30x-16=0 $

$ \Rightarrow $ $ 2x^{2}-15x-8=0 $

$ \Rightarrow $ $ 2x(x-8)+1(x-8)=0 $

$ \Rightarrow $ $ (x-8)(2x+1)=0 $ $ x=8km/h $ Hence, speed of motorboat in still water is $ 8km/h. $

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