Question

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hour it can go 40 km upstream and 55 km downstream. If speed of the boat in still water is x km/hr and speed of stream be y km/hr, then - (1) x = 8 (2) y = 4 (3) x = 3 (4) y = 8

Answer 1

Hey

Here is your answer,

Let the speed of the stream be = u kmph
let the speed of the boat be = v kmph

speed upstream will be = v - u  kmph
speed downstream will be =  v + u  kmph

30 km  upstream in time duration  =   30 / (v - u)  hrs
44 km  down stream in time duration  =  44 / (v + u)  hrs

       44 / (v + u)  + 30 / (v -u)  = 10 hrs     --- (1)

Similarly,

      40 /(v - u)  + 55 / (v +u)  = 13 hrs         Multiply with 3/4:  
      30/(v-u) + 165 / 4(v+u) =    39/4        --- (2) 

Now (1) - (2)  =>    [44 - 165/4] / (v+u) = 10 - 39/4 = 1/4
                   =>     v + u = 11      --- (3)
Substitute this in (1) to get: 
             44/11 + 30/(v-u) = 10
           =>  v - u = 30/6 = 5      --- (4)

Solving  (3) and (4) ,  we get :  v = 8 kmph    and  u = 3 kmph

The correct options are (3) and (4).

Hope it helps you!
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