Question

Q62. The speed of a boat in still water is 10 kmph. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is (a) 2 kmph (b) 2.5 kmph (c) 3 kmph (d) 4 kmph

Answer 1

Given that  

Speed of boat in water = 10 km/h  

Distance of downstream = 26 km  

Distance of upstream = 14 km  

To find  

The speed of stream = ?

  Assumption  

 Let x be the speed of stream = x km/h  

Then, downstream speed = $\frac{26}{10+x}$

And, upstream speed = $\frac{14}{10-x}$

 But according to our question,  

The time of each stream is The time of each stream is equal, so,  

 $\frac{26}{10+x} = \frac{14}{10-x}$

  $=> 26(10-x) = 14(10+x)$  

 $=> 260 - 26x = 140 + 14x$  

 $=> 260 - 140 = 14x + 26x$

  $=> 120 = 40x$  

 $=> \frac{120}{40} = x$  

 $=> \frac{12\cancel{0}}{4\cancel{0}} = x$  

 $=> \frac{12}{4} = x$

  $=> \frac{\cancel{12}}{\cancel{4}} = x$

  $=> 3 = x$

  But, x is assumed as the speed of the stream.  

  ∴ The speed of the stream = 3 km/h

 So, option (c) 3 km/h is correct.