GATE 2016 EC (EC2) – Question 9

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

M and N start at the same location. M travels 10 km east, then 10 km northeast. N travels 5 km south, then 4 km southeast. The shortest distance between their final positions, in km, is

18.60
22.50
20.61
25.00

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Show answer and explanation

Correct answer: (C) 20.61

Explanation

Take east and north as positive axes. M finishes at $(10+10/\sqrt2,10/\sqrt2)$ and N at $(4/\sqrt2,-5-4/\sqrt2)$.

Their coordinate differences are $10+3\sqrt2$ and $5+7\sqrt2$. Thus distance squared is $(10+3\sqrt2)^2+(5+7\sqrt2)^2=241+130\sqrt2$.

The distance is **20.6118 km**, closest to **20.61, C**.

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