Laxmi goes 6 km towards South-East from her office.Then she goes 15 km turning to West. After this she goes 6 km towards North-West and in the end she goes 11 km towards East. How far is she from her office ?
Answer: C
Correct answer: 4 km
Resolve the diagonal legs into components, using \( 6/\sqrt{2} = 4.24 \). South-east 6 gives \( (4.24,-4.24) \); west 15 gives \( (-10.76,-4.24) \); north-west 6 adds \( (-4.24,+4.24) \) and gives \( (-15,0) \); east 11 gives \( (-4,0) \). The two diagonal legs are equal and opposite, so they cancel exactly and only the east-west legs survive: \( 15-11 = 4 \) km. Spotting that cancellation removes the need for any arithmetic with surds at all.
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