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 $\, km$)

In a square arrangement,let the initial positions be $A$ (North-West),$B$ (North-East),$C$ (South-East),and $D$ (South-West). $C$ and $A$ move diagonally to opposite corners and then one side each clockwise and anticlockwise respectively. $B$ and $D$ move two sides each clockwise and anticlockwise respectively. Who is at the North-West corner?

Point $D$ is $14 \,m$ towards the West of point $A.$ Point $B$ is $4 \,m$ towards the South of point $D.$ Point $F$ is $9 \,m$ towards the South of point $D.$ Point $E$ is $7 \,m$ towards the East of point $B.$ Point $C$ is $4 \,m$ towards the North of point $E.$ Point $G$ is $4 \,m$ towards the South of point $A.$ $A$ is in which direction with respect to $C$?

From the positions in the original figure,$C$ and $A$ move diagonally to opposite corners and then one side each clockwise and anticlockwise respectively. $B$ and $D$ move two sides each clockwise and anticlockwise respectively. Where is $A$ now?

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?

Sachin and Vinod want to visit the museum after their exams. Sachin's exams finish on $9^{th}$ April and he is leaving for a holiday on $12^{th}$ April. Vinod's exams will be over by $10^{th}$ April,after which he is free. On which of the following dates can the two definitely meet?