Alcohol	:	Water
	4	:	3
Let	4x	:	3x

∴ 5 litres of water is added to the mixture \begin{align} & \Rightarrow \frac{{4x}}{{3x + 5}} = \frac{4}{5} \cr & \Rightarrow 20x = 12x + 20 \cr & \Rightarrow 8x = 20 \cr & \Rightarrow x = \frac{{20}}{2} \cr & \Rightarrow x = \frac{5}{2} \cr & {\text{Quantity of alcohol}} \cr & \Rightarrow {\text{4}} \times \frac{5}{2} = 10\, {\text{litres}} \cr\end{align}

\begin{align} & {\text{Remainder}} \cr & = {\text{Rs}}{\text{.}}\left[ {{\text{1087}} - \left( {10 + 12 + 15} \right)} \right] \cr & = {\text{Rs}}{\text{. }}1050. \cr & \therefore {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {1050 \times \frac{7}{{21}}} \right) + 12} \right] \cr & = {\text{Rs}}{\text{. }}362. \cr\end{align}

\begin{align} & p = k, \, q = 2k, \, r = 4k. \cr & {\text{Then, }} \cr & \sqrt {5{p^2} + {q^2} + {r^2}} \cr & = \sqrt {5{k^2} + {{\left( {2k} \right)}^2} + {{\left( {4k} \right)}^2}} \cr & = \sqrt {5{k^2} + 4{k^2} + 16{k^2}} \cr & = \sqrt {25{k^2}} \cr & = 5k \cr & = 5p. \cr\end{align}

Each exterior angle of n sided polygon is ${\text{ = }}\left( {\frac{{360}}{n}} \right)$ And each interior angle of n sided polygon \begin{align} & {\text{ = }}\frac{{\left( {n - 2} \right) \times 180}}{n} \cr & \therefore \frac{{\frac{{\left( {n - 2} \right) \times 180}}{n}}}{{\frac{{360}}{n}}} = \frac{2}{1} \cr & \Rightarrow \frac{{\left( {n - 2} \right)}}{2} = 2 \cr & \Rightarrow n - 2 = 4 \cr & \Rightarrow n = 6 \cr\end{align}

Girls:boys = 6:5;

Hence, girls = 6*66/11 = 36;

Boys = 30;

New ratio, 30:(36+4) = 3:4.