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. $
BETA
