Q. A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point?
(a) An angle less than 45o South of East
(b) An angle less than 45o North of East
(c) An angle more than 45o South of East
(d) An angle more than 45o North of East
Correct Answer: (b) An angle less than 45o North of East
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
We can visualize the woman’s movements on a coordinate plane. Let’s say she starts at the origin (0,0). When she runs 12 km towards her North, her position changes to (0,12). Then when she runs 6 km towards her South, her position changes to (0,6). Finally when she runs 8 km towards her East, her position changes to (8,6).
Now we can use the Pythagorean theorem to find the distance between her starting point and ending point. The distance is sqrt((8-0)^2 + (6-0)^2) = 10 km.
To find the direction from her starting point to her ending point we can use trigonometry. The angle is tan^-1(6/8) = 36.87 degrees. (Tan 45 degree = 1)
6/8 is less than 1, So angle will be less.
So the woman is at an angle less than 45 degrees North of East from her starting point. So the correct answer is (b) An angle less than 45o North of East.
