MBApyq

Shyam Salesman Walking Directions

XAT 2012 · Quantitative Ability & Data Interpretation · Medium · Geometry

All XAT 2012 questionsMore Geometry questionsAll XAT QADI

Shyam, a fertilizer salesman, sells directly to farmers. He visits two villages A and B. Shyam starts from A, and travels 50 meters to the East, then 50 meters North-East at exactly 45° to his earlier direction, and then another 50 meters East to reach village B. If the shortest distance between villages A and B is in the form of ab+ca\sqrt{b+\sqrt{c}} meters, Find the value of a+b+c.

  1. A.

    52

  2. B.

    54

  3. C.

    58

  4. D.

    59

  5. E.

    None of the above.

Answer

E

Explanation

Net horizontal displacement x=50+50cos⁡45∘+50=100+252x = 50 + 50\cos 45^\circ + 50 = 100 + 25\sqrt{2}. Net vertical displacement y=50sin⁡45∘=252y = 50\sin 45^\circ = 25\sqrt{2}. Shortest distance d=x2+y2=(100+252)2+(252)2=10000+50002+1250+1250=12500+50002=505+22=505+8d = \sqrt{x^2 + y^2} = \sqrt{(100 + 25\sqrt{2})^2 + (25\sqrt{2})^2} = \sqrt{10000 + 5000\sqrt{2} + 1250 + 1250} = \sqrt{12500 + 5000\sqrt{2}} = 50\sqrt{5 + 2\sqrt{2}} = 50\sqrt{5 + \sqrt{8}}. So a=50,b=5,c=8a = 50, b = 5, c = 8. a+b+c=50+5+8=63a+b+c = 50 + 5 + 8 = 63. Since 63 is not among options A-D, option E (None of the above) is correct.

Related Geometry questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace