Question: A boat covers 12 km upstream and 18 km downstream in 3 h, while it covers 36 km upstream and 24 km downstream in $ 6\frac{1}{2}h. $ What is the speed of the current?
Options:
A) 1.5 km/h
B) 1 km/h
C) 2 km/h
D) 2.5 km/h
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] If the speed of boat in still water be x km/h and speed of current by $ ykm/h. $
Then, speed in downstream $ =(x+y) $
Speed in upstream $ =(x-y) $
According to the question,
$ \frac{12}{x-y}+\frac{18}{x+y}=3 $
. (i)
$ \frac{36}{x-y}+\frac{24}{x+y}=\frac{13}{2} $
. (ii)
On multiplying Eq. (i) by 3 and subtracting Eq. (ii) from Eq. (i),
$ \frac{54}{x+y}-\frac{24}{x+y}=9-\frac{13}{2} $
$ \Rightarrow $ $ \frac{30}{x+y}=\frac{5}{2} $
$ \Rightarrow $ $ x+y=12 $
(iii)
On substituting the value $ (x+y) $ of from Eq. (iii), we get $ \frac{12}{x-y}+\frac{18}{12}=3 $
$ \Rightarrow $ $ \frac{12}{x-y}=3-\frac{3}{2}=\frac{3}{2} $
$ \Rightarrow $ $ x-y=\frac{12\times 2}{3}=8 $
. (iv)
Speed of current $ =\frac{1}{2} $ (speed downstream
- Speed upstream)
$ =\frac{1}{2}(12-8)=2,km/h $
BETA
