Question

A. A boat travels 300 metres upstream .
B. it's speed downstream is 8/5 times it's speed upstream .
which of the following option provides correct relationship between speed of current and speed of boat ?​

Answer 1

Answer:

speed of current=3/13 of speed of boat

b is the correct option.

Step-by-step explanation:

Let speed of the boat = x m/min

and speed of current = y m/min

Therefore, we have

Upstream speed = (x-y)

Downstream speed = (x+y)

Now, it has been given that boat travels 300 m upstream in 15 mins. Thus, we have the equation

\begin{gathered}x-y=\frac{300}{15}\\\\x-y=20...(i)\end{gathered}

x−y=

15

300

x−y=20...(i)

Now, the second condition is speed downstream is 8/5 time its upstream . Thus, the other equation is

x+y=\frac{8}{5}\cdot(x-y)x+y=

5

8

⋅(x−y)

From equation (i)

\begin{gathered}x+y=\frac{8}{5}\cdot20\\\\x+y=32....(ii)\end{gathered}

x+y=

5

8

⋅20

x+y=32....(ii)

Now, add equation (i) and (ii)

2x=52

x = 26

Plugging this value in (i)

26-y=20

y = 6

Therefore, we have

speed of boat = 26 m/min

speed of current = 6 m/min

Now, we find the relation between these two speeds

\begin{gathered}\frac{6}{26}\\\\=\frac{3}{13}\end{gathered}

26

6

=

13

3

Thus, we can conclude that

speed of current=3/13 of speed of boat

b is the correct option.