A woman leaves her home. She walks 40 m in North-West direction and then 90 m in South-East direction. Then, she moves 30 m in North direction. How far is she now from her initial position?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 40 m
Note: The given answer is as per the official NTA Answer Key. However, none of the given options appears to be correct, because her final distance from home works out to about 35.8 m, as explained below.
North-West and South-East are opposite directions, so the first two walks lie on one straight line through her home. 40 m out and 90 m back leave her \(90-40=50\) m South-East of home (point B). The 30 m walk North then starts from B.
Position of B (a South-East line makes \(45^\circ\) with both East and South):
East of home \(\displaystyle =\frac{50}{\sqrt{2}}\approx35.36\) m
South of home \(\displaystyle =\frac{50}{\sqrt{2}}\approx35.36\) m
After the 30 m walk North:
East of home: still 35.36 m
South of home: \(35.36-30=5.36\) m
Distance from home \(=\sqrt{35.36^2+5.36^2}=\sqrt{1250+28.7}\approx35.8\) m
The answer 40 m comes from \(\sqrt{50^2-30^2}\), which treats the 50 m and the 30 m as two sides of a right triangle with the 50 m as the hypotenuse. That needs a right angle at the point where she ends, but the walk North makes an angle of \(45^\circ\) with the line from B back to her home, and the triangle formed has no right angle. NTA’s key added about 4 metres that the woman never walked.