Subject: General Aptitude · Chapter: Boats and Streams · Exam: · Marks: · Difficulty:
Boat A travels downstream from Point X to Point Y in 3 hours less than the time taken by Boat B to travel upstream from Point Y to Point Z. The distance between X and Y is 20 km, which is half of the distance between Y and Z. The speed of Boat B in still water is 10 km/h and the speed of Boat A in still water is equal to the speed of Boat B upstream. What is the speed of Boat A in still water? (Consider the speed of the current to be the same.) [RBI Gr. 'B' (Phase I) Exam, 2015]
(a)10 km/h
(b)16 km/h
(c)12 km/h
(d)8 km/h
Answer
Answer (as printed): D
Explanation
Let the speed of current in water $=\mathrm{s} \mathrm{km} / \mathrm{h}$ The time taken by boat $\mathrm{A}=t_{a}$ And the time taken by boat $\mathrm{B}=t_{b}$ Distance between point $X$ to point $Y=20 \mathrm{km}$ Distance between point Y to Point $\mathrm{Z}=40 \mathrm{km}$ According to the question $$\frac{40}{t_{b}}=10+s$$ $t_{a}=t_{b} 3$ The speed of boat A in still water = The speed of boat B in upstream = (10 + s) km/h So, $t_{\mathrm{a}}=20 / 10=2$ hours Hence, $t_{b}=t_{a}+3=2+3=5$ hours. By using equation (i) $$\begin{aligned} & \frac{40}{5}=10+\mathrm{S} \\ \Rightarrow \quad & 8=10+\mathrm{S} \\ & \mathrm{S}=2 \mathrm{km} / \mathrm{h} \end{aligned}$$ The speed of boat A in still water $=(10-2)=8 \mathrm{km} / \mathrm{h}$