Question

A boat takes $7$ hours to travel $30km$ upstream and $28km$ downstairs. It takes $5$ hours to travel $21km$ upstream and to return back. Find the speed of the boat in still water.

• A. $10$ $km/hr$
• B. $20$ $km/hr$
• C. $14$ $km/hr$
• D. $6$ $km/hr$

Answer 1

The correct option is A $10$ $km/hr$

Let speed of Boat $=x$ kmph
speed of water $=y$ kmph
$\therefore \frac{30}{x-y}+\frac{28}{x+y}=7$ ........ $\left(1\right)$ and
$\frac{21}{x+y}+\frac{21}{x-y}=5$ ......... $\left(2\right)$
Solving this,
We get $x+y=14$ ......... $\left(3\right)$ and
$x-y=6$ .......... $\left(4\right)$
$\therefore$ Solving again we get,
$x=10$ and $y=4$
$\therefore$ speed of boat $=10$ kmph.

Hence, option A is correct.