Let the speed of the boat in still water be ' \(x\) ' km/hr and speed of the stream be ' \(y\) ' \(\mathrm{km} / \mathrm{hr}\).
\(\therefore\) Speed of boat up stream - \((x-y) \mathrm{km} / \mathrm{hr}\).
Speed of boat down stream : \((x+y) \mathrm{km} / \mathrm{hr}\).
$$
\begin{aligned}
\therefore \quad \frac{30}{x-y}+\frac{28}{x+y} &=7 \\
\text { and } \quad \frac{21}{x-y}+\frac{21}{x+y} &=5 \\
\text { Let } \frac{1}{x-y} \text { be } a \text { and } \frac{1}{x+y} \text { be } b \\
30 a+28 b=7 \\
21 a+21 b=5 \quad \ldots \text { (ii) }
\end{aligned}
$$
Multiplying eqn. (i) by 3 and eqn. (ii) by 4 and then subtracting,
..(iii)
\(\ldots\) (iv)
\(\begin{aligned} 6 a &=1 \\ a &=\frac{1}{6} \\ \text { Putting this value of } a \text { in eqn., (i), } \\ 30 \times \frac{1}{6}+28 b &=7 \\ 28 b &=7-30 \times \frac{1}{6}=2 \\ b &=\frac{1}{14} \\ x+y &=14 \end{aligned}\)
$$
6 a=1
$$
\(\ldots(i v)\)
Now,
$$
a=\frac{1}{x-y}=\frac{1}{6}
$$
\(\therefore\)
\(\therefore\)
