Subject: General Aptitude · Chapter: Boats and Streams · Exam: · Marks: · Difficulty:
A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?
(a)160 km
(b)180 km
(c)200 km
(d)220 km
Answer
Answer (as printed): B
Explanation
Speed downstream $=(14+4) \mathrm{km} / \mathrm{hr}=18 \mathrm{km} / \mathrm{hr}$; Speed upstream $=(14-4) \mathrm{km} / \mathrm{hr}=10 \mathrm{km} / \mathrm{hr}$. Let the distance between A and B be $x \mathrm{km}$. Then, $\frac{x}{18}+\frac{(x / 2)}{10}=19 \Leftrightarrow \frac{x}{18}+\frac{x}{20}=19$ $$\Leftrightarrow \frac{19 x}{180}=19 \Leftrightarrow x=180 \mathrm{km} .$$