question_answer

A, B and C are situated at the bank of river which is flowing at a constant rate. B is at an equal distance with A and C. A swimmer Avinash takes 10 h to swim from A to B and B to A. Also, he takes 4 h to swim from A to C. What is the ratio of speed of Avinash in still water and speed of stream?

A) 5 : 3     

B) 3 : 5  

C) 2 : 5                             

D) 1: 2

Correct Answer: A

Solution :

Let speed of Avinash in still water be a km/h and speed of stream be b km/h.

Let \[AB=BC=x\,\,km\]

From first condition,

\[\frac{x}{a+b}+\frac{x}{a-b}=10\]                  ... (i)

From second condition,

\[\Rightarrow \]   \[\frac{x}{a+b}=2\]                              (ii)

On putting the value in Eq. (i), we get

\[2+\frac{x}{a-b}=10\]

\[\Rightarrow \]   \[\frac{x}{a-b}=8\]                                (ii)

On dividing Eq. (iii) by Eq. (ii), we get

\[\frac{a+b}{a-b}=\frac{8}{2}=4\]

\[\Rightarrow \]   \[a+b=4a-4b\]\[\Rightarrow \]\[3a=5b\]

\[\therefore \]      \[a:b=5:3\]