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Find the speed of the man in still water ?

I. The downstream speed is $12$ km/hr.

II. The upstream speed is $4$ km/hr.

III. In a back-and-forth travel between two points, $A$ and $B$ , the average speed of the man was $6$ km/hr.

A) I and II only

B) All I, II and III

C) III, and either I or II

D) Any two of the three

E) None of these

Option D

From I and II, speed of the man in still water $=\frac{1}{2}(12+4)$ $=8$ km/hr.

From II and III, we get:

Average speed $=\frac{2xy}{x+y}$

$\Rightarrow \frac{2\times 4\times y}{4+y}$ $=6$

$\Rightarrow 8y$ $=24+6y$

$\Rightarrow y$ $=12$ .

$\therefore$ Required speed $=\frac{1}{2}(12+4)$ km/hr $=8$ km/hr.

Similarly, I and III also give the answer.

$\therefore$ Correct answer is (D).

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