It is given that
Ratio of three numbers \[=\text{ }1/2:\text{ }1/3:\text{ }1/4\]
\[\begin{array}{*{35}{l}}
=\text{ }\left( 6:\text{ }4:\text{ }3 \right)/\text{ }12 \\
=\text{ }6:\text{ }4:\text{ }3 \\
\end{array}\]
Consider first number = \[6x\]
Second number = \[4x\]
Third number = \[3x\]
So based on the condition
\[\begin{array}{*{35}{l}}
{{\left( 6x \right)}^{2}}~+\text{ }{{\left( 4x \right)}^{2}}~+\text{ }{{\left( 3x \right)}^{2}}~=\text{ }244 \\
36{{x}^{2}}~+\text{ }16{{x}^{2}}~+\text{ }9{{x}^{2}}~=\text{ }244 \\
\end{array}\]
So we get
\[\begin{array}{*{35}{l}}
{{\left( 6x \right)}^{2}}~+\text{ }{{\left( 4x \right)}^{2}}~+\text{ }{{\left( 3x \right)}^{2}}~=\text{ }244 \\
36{{x}^{2}}~+\text{ }16{{x}^{2}}~+\text{ }9{{x}^{2}}~=\text{ }244 \\
\end{array}\]
Here
First number \[=\text{ }6x\text{ }=\text{ }6\text{ }\times \text{ }2\text{ }=\text{ }12\]
Second number \[=\text{ }4x\text{ }=\text{ }4\text{ }\times \text{ }2\text{ }=\text{ }8\]
Third number \[=\text{ }3x\text{ }=\text{ }3\text{ }\times \text{ }2\text{ }=\text{ }6\]