Going $50 \,m$ to the South of her house,Radhika turns left and goes another $20 \,m.$ Then,turning to the North,she goes $30 \,m$ and then starts walking to her house. In which direction is she walking now?

Laxman went $15 \, km$ to the west from my house,then turned left and walked $20 \, km$. He then turned east and walked $25 \, km$ and finally turned left and covered $20 \, km$. How far was he from his house? (in $\, km$)

$A$ man walks $6 \, km$ to the east and then turns to the south and walks $5 \, km$. Again he turns to the east and walks $6 \, km$. Next,he turns towards north and walks $10 \, km$. How far is he now from his starting point (in $, km$)?

$I$ am facing east. $I$ turn $100^{\circ}$ in the clockwise direction and then $145^{\circ}$ in the anticlockwise direction. Which direction am $I$ facing now?

$A$ man leaves for his office from his house. He walks towards east. After moving a distance of $20 \, m$,he turns towards south and walks $10 \, m$. Then he walks $35 \, m$ towards west and further $5 \, m$ towards north. He then turns towards east and walks $15 \, m$. What is the straight distance in metres between his initial and final positions?

Rama remembers that she met her brother on Saturday,which was after the $20^{th}$ day of a particular month. If the $1^{st}$ day of that month was Tuesday,then on which date did Rama meet her brother?