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 |
\[\frac{a+b}{a-b}=\frac{8}{2}=4\] |
\[\Rightarrow \] \[a+b=4a-4b\]\[\Rightarrow \]\[3a=5b\] |
\[\therefore \] \[a:b=5:3\] |
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