Directions : In the following question consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statement (s) is/are necessary to answer the question.
What is the speed of boat in still water?
I. The boat covers 12 km in 2 hours in downstream.
II. The boat covers same distance in 4 hours in upstream.
III. The speed of stream is one third of that of boat in still water.
Both I and II
All I, II and III
Question cannot be answered even with the information in all three statements.
I and either II or III
None of these
Solution
From statements I and II,
Rate downstream
= u + v = 6 kmph
Rate upstream = u – v
= 3 kmph
U $= \dfrac{1}{2}((u + v)(u - v))$
$= \dfrac{1}{2}(6+3)$
$= \dfrac{9}{2}$ kmph
From statements I and III,
u + v = 6 kmph
$\Rightarrow u + \dfrac{u}{3} = 6$
$\Rightarrow~4u = 18$
$\Rightarrow~u~= \dfrac{18}{4} = \dfrac{9}{2}$ kmph