$T _{ C } \cos 30^{\circ}= T _{ S } \cos 60^{\circ}$

$T _{ C } \times \frac{\sqrt{3}}{2}= T _{ S } \times \frac{1}{2}$

$\sqrt{3} T _{ C }= T _{ S } \ldots . \text { (i) }$

in $y$ direction

$T _{ C } \sin 30^{\circ}+ T _{ S } \sin 60^{\circ}=100$

$\frac{ T _{ C }}{2}+\frac{ T _{ S } \sqrt{3}}{2}=100 \ldots . \text { (ii) }$

Solving equation $(i)$ & $(ii)$

$T _{ C }=50 N$

$T _{ S }=50 \sqrt{3} N$

We know

$\Delta L =\frac{ FL }{ AY }$

$=\frac{\Delta L _{ C }}{\Delta L _{ S }}=\frac{ T _{ C } L _{ C }}{ A _{ C } Y _{ C }} \times \frac{ A _{ S } Y _{ S }}{ T _{ S } L _{ S }}$

On solving above equation

$\frac{\Delta L _{ C }}{\Delta L _{ S }}=2$

Ans. $2.00$