A boat goes 30 km upstream and 44 km downstream in a total of 10 hours. It also goes 40 km upstream and 55 km downstream in a total of 13 hours. The speed of the stream is:

Correct option is C

Given:

Total time taken by boat to go 30km upstream and 44km downstream= 10hours

Total time taken by boat to go 40km upstream and 55km downstream =13hours

Formula Used:

If speed of boat is u and spped of stream is v

Then speed of boat upstream = (u-v)

Speed of boat downstream = (u+v)

Solution:

According to question:

Let the speed of boat upstream be x and downstream be y

Then

​$$\frac{30}{u-v} + \frac{44}{u+v} = 10$$​​

​$$\frac{40}{u-v} + \frac{55}{u+v} = 13$$​​

Let $$\frac{1}{u-v} = x \text{ and } \frac{1}{u+v} = y$$​​

Then

30x+44y = 10    ...(1)

40x+55y = 13    …(2)

Solving eq(1) and eq(2)

We get $$y=\frac{1}{11}\text{ and }x= \frac{1}{5}$$​​

​$$\frac{1}{u-v} = \frac{1}{5}\text{ and }\frac{1}{u+v} =\frac{1}{11}$$​​

u-v = 5

u+v = 11

Solving we get u= 8km/hr and v =3km/hr

Hence speed of stream = 3km/hr