Given below are two statements based on the following:
A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours.
Statement I: Speed of the boat in still water is 12 km per hour.
Statement II: Speed of the stream is 4 km per hour.
In the light of the above statements, choose the correct answer from the options given below:

Let the speed of boat in still water be B, and the speed of stream be R.

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours.

$$\dfrac{30}{B-R}+\dfrac{28}{B+R}=7$$

It can travel 21 km upstream and return in 5 hours.

$$\dfrac{21}{B-R}+\dfrac{21}{B+R}=5$$

Let $$\dfrac{1}{B-R}=x$$ and $$\dfrac{1}{B+R}=y$$

$$30x+28y=7\rightarrow1$$
$$21x+21y=5\rightarrow2$$

Multiply eq. 1 by 3 and eq. 2 by 4, and then subtract -

$$90x-84x=21-20$$

$$x=\dfrac{1}{6}$$

Therefore, $$y=\dfrac{1}{14}$$

Thus, $$B+R=14$$ and $$B-R=6$$

$$B=10$$ kmph and $$R=4$$ kmph

Therefore, speed of boat is 10 km/h and speed of stream is 4 km/h.