Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 5 km in that direction. She then goes North for 8 km. How far is she from point P, and in which direction should she go to reach point P?
A. 8 km, North
B. 12 km, North
C. 6 km, North
D. 10 km, North
GATE 2017 · General Aptitude · Direction Sense · medium
Answer: A. 8 km, North
Set up coordinates and locate Q: P = (0, 0). After North 3 km: (0, 3). After East 4 km: (4, 3) = Q.
Compute distance PQ: PQ = 5 km. Fatima faces P from Q and walks exactly 5 km, arriving back at P = (0, 0).
Walk North 8 km from P: Fatima is now at (0, 8), which is 8 km directly north of P.
Determine distance and direction from P: She is 8 km North of P. To reach P she must go South.