A man moves 24 metres in South direction and turns 90 degrees anticlockwise and moves another 7 metres and takes a right turn and moves 3 metres and then moves 3 metres in the North direction. Find the distance between his initial and his final position.

Let's track the man's movement step-by-step from the starting point (0,0):
Moves 24 m South: Reaches (0,−24).

Turns 90
∘
anticlockwise (faces East) and moves 7 m: Reaches (7,−24).

Takes a right turn (now faces South) and moves 3 m: Reaches (7,−27).

Moves 3 m North: He retraces his last vertical step upwards and returns to (7,−24).

Now, find the straight-line distance between the initial position (0,0) and the final position (7,−24):

Distance=
(7−0)
2
+(−24−0)
2


​

Distance=
7
2
+(−24)
2


​
=
49+576

​
=
625

​
=25 m
Therefore, the distance between his initial and final position is 25 m.