Question

A boat goes 24 km upstream and 28 km down stream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is

• A. 10 km/hr
• B. 4 km/hr
• C. 14 km/hr
• D. 6 km/hr

Answer 1

Answer: (A)

10 km/hr

Let speed of boat in still water be a km/hr.
Let rate of the current be b km/hr.
$\therefore$ Speed of the boat upstream $=(a-b)$ km/hr.
$\therefore \frac{24}{a-b}+\frac{28}{a+b}=6$ ...(i)
and $\frac{30}{a-b}+\frac{21}{a+b}=\frac{13}{2}$ ..(ii)
From (i) and (ii), we have
$\frac{1}{a-b}=\frac{1}{6}$ and $\frac{1}{a+b}=\frac{1}{14}$
$\Rightarrow a-b=6$ and $a+b=14$
$\Rightarrow a=10$ km/hr.