Question : A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
Option 1: 6 km/h
Option 2: 10 km/h
Option 3: 8 km/h
Option 4: 7 km/h
Correct Answer: 8 km/h
Solution :
Let the speed of the boat in still water be $x$ km/h and
The speed of stream = $y$ km/h
Speed of boat at downstream = $(x+y)$ km/h
Speed of boat at upstream = $(x−y)$ km/h
Time taken to cover 20 km upstream = $\frac{20}{x-y}$
Time taken to cover 44 km downstream = $\frac{44}{x+y}$
According to the question,
$\frac{20}{x-y}+ \frac{44}{x+y} = 8$ .......(1)
Also,
$\frac{15}{x-y}+ \frac{22}{x+y} = 5$ .......(2)
Now let $\frac{1}{x-y} = u$ and $\frac{1}{x+y} = v$
$\therefore$ equation (1) and (2) becomes,
$20u + 44v = 8$
$15u +22v = 5$
Solving these equations, we get
$u = \frac{1}{5}$
$v = \frac{1}{11}$
⇒ $x-y = 5$ and $x+y = 11$
$\therefore$ $x = 8$ and $y = 3$
The speed of the boat in still water = $x$ = 8 km/h
Hence, the correct answer is 8 km/h.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CGL
