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 $\, km$)

$A$ boy rode his bicycle northwards,then turned left and rode $1 \, km$,and again turned left and rode $2 \, km$. He found himself exactly $1 \, km$ west of his starting point. How far did he ride northwards initially? (in $km$)

From the original position given in the above figure,$A$ and $B$ move one arm length clockwise and then cross over to the corner diagonally opposite; $C$ and $D$ move one arm length anti-clockwise and cross over the corner diagonally opposite. The original configuration $ADBC$ has now changed to

From the positions in the original figure,$A$ and $C$ move diagonally to opposite corners and then one side each clockwise and anticlockwise respectively. $D$ and $B$ move two sides each clockwise and anticlockwise respectively. Where is $A$ 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 turning left,covered $20 \, km$. How far was he from my house? (in $\, km$)

One morning after sunrise,Vishakh and Satheesh were standing in a lawn with their backs towards each other. Vishakh's shadow fell exactly towards his left-hand side. Which direction was Satheesh facing?