Question

20. A boat goes a certain distance downstream and then returns and
covers 40% of distance covered in downstream. Ratio of time taken in
covering downstream and upstream distances is 3 : 2. If speed of boat
in still water is reduced by 50% then it covers 60 km downstream in
10 hours. Find the speed of boat in still water.
(a) 9 km/hr
(b) 8 km/hr
(c) 6 km/hr
(d) 10 km/hr
(e) 12 km/hr
​

Answer 1

Solution:

Let speed of boat in still water be m km/hr

Let speed of boat currently be n km/hr

And as it is given that ratio of time taken in  covering downstream and upstream distances is 3 : 2.

So , Let the time taken to cover the given distance in downstream and upstream be 3t hours and 2t hours

Now ,

40% of distance is covered in = 2t hours

100% of distance is covered in = 5t hours

According to question,

$\frac{m - n}{m + n} = \frac{3}{5}$

$5m - 5n = 3m + 3n$

$\frac{m}{n} = \frac{4}{1}$

Now ,

$\frac{60}{\frac{m}{2} + n } = 10$

$\frac{m}{2} + n = 6$

$\frac{4n}{2} + n = 6$

$6n = 12$

$n = 2 km/hr$

So ,

$\frac{m}{n} = \frac{4}{1}$

$\frac{m}{2} = \frac{4}{1}$

$m = 8 km/hr$

(b) 8 km/hr is the correct answer.

The speed of boat in still water will be 8 km/hr.

Answer 2

Given :

Ratio of time taken in covering downstream and upstream distance is =3:2

Speed of boat in still water at downstream = 60 km

Time taken = 10 hours

Reduced speed of boat in still water covered by 50%

Return speed of downstream 40%

To find:

                Speed of boat in still water =??

  Solution :

                 Speed of boat in still water = x km/hr

                 Actual speed of boat = y km/hr

                Speed of boat downstream = x-y

               Total speed of boat = x+ y

               Ratio of time taken $\frac{3}{2}$

               40% distance covered in 2t hr

              Total distance covered in 3t + 2 t = 5t hr

       $\frac{x-y}{x+y} = \frac{3}{5}$

             5x-5y = 3x – 3y

               After solving  we get:

             2x = 8y

             $\frac{x}{y}$= 4

             Now

            $\frac{60}{(x/2 + y)}$ = 10

            After doing simple calculation

             Y= 2km/hr

           And X= 8km/hr

       

     So the speed of boat in still water = 8km/hr