Time, Speed & Distance
Aptitude

 Back to Questions
Q.

The $XYZ$ river flows at 12 km/hr. A boy who can row at $\frac{25}{18}$ m/s in still water had to cross it in the least possible time. The distance covered by the boy is how many times the width of the river $XYZ$?

 A.

2.1

 B.

2.3

 C.

2.6

 D.

2.9

 Hide Ans

Solution:
Option(C) is correct

Speed of the river $XYZ = 12$ kmph

Speed of the boy = 5 kmph

Let the time taken by the boy to cross the river in still water = $T$

Width of the river = $5T$ 

The boy takes the least time when he is travelling directly across the river.

But the river current pushes him in a direction perpendicular to the flow, 

Distance travelling along the river = $12T$

Effective distance travelled by boy

\(=\sqrt{(12T)^2+(5T)^2}\)

\(=13T\)

\(\Rightarrow \dfrac{\text{Distance covered by the boy}}{\text{width of the river}}\)

\(=\dfrac{13T}{5T}\)

\(=2.6\)

Edit: Thank you Ravi, modified the question and added rowing velocity of the boy.


(5) Comment(s)


Dhanabalavignesh
 ()

how is the width of the river is taken as 5T



Prateek
 ()

Shouldn't the boy's speed be 25/18 kmph?


Deepak
 ()

Thank you Prateek for notifying, corrected the rowing speed of boy.


Ravi
 ()

Speed at which boy rows in the river is not mentioned, kindly look into this.


Deepak
 ()

Thank for notifying, modified the question...