Direction : Read the given information carefully and answer the questions…

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Direction : Read the given information carefully and answer the questions given beside: (A set of 2 questions)

Kishore and Lokesh are siblings and live in the same room. Both of them went to their respective

colleges from different routes. Colleges of both Kishore and Lokesh are in east direction with respect

to their room.

Kishore moves 150m in north direction and turns right. After walking for 110m, he reached Axis bank. Then he turns right and move 70m to reach a traffic signal. Then he turns left and move 140m to reach the shopping mall. Then finally he moves 100m in south west direction to his college. What is the shortest distance between Axis bank and his college?

  1. A.

    150 m

  2. B.

    160 m

  3. C.

    170 m

  4. D.

    180 m

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Concept: In direction-and-distance puzzles, model every walked leg as a displacement on the coordinate plane — North/South changes the y-coordinate, East/West changes the x-coordinate. Once every landmark is plotted as a point (x, y) relative to a fixed origin, the shortest (straight-line) distance between any two points is the hypotenuse given by the distance formula, which comes from the Pythagorean theorem.

Application

  1. Fix Kishore's room at the origin (0, 0).

  2. He walks 150 m north, then turns right (east) and walks 110 m to reach Axis Bank — so Axis Bank sits at (110, 150).

  3. From Axis Bank he turns right (south) and walks 70 m to the traffic signal, placing it at (110, 80).

  4. He then turns left (east) and walks 140 m to the shopping mall, so the mall is at (250, 80).

Colleges of both Kishore and Lokesh are in east direction with respect to their room:

Therefore, Kishore's college is exactly in the east direction of Kishore's room — i.e. it sits at the same y-level as the room, y = 0:

Note: “south-west” here fixes only the general quadrant of travel, not a fixed 45° angle — its exact horizontal and vertical components are pinned down by the given constraint that the college lies due east of the room.

  1. On the final 100 m south-west leg from the mall, the vertical (south) component must therefore bring the y-coordinate from 80 down to 0 — a drop of 80 m.

  2. Treating the 100 m walk as the hypotenuse of a right triangle with one leg 80 m, the horizontal (west) leg follows from Pythagoras: √(1002 − 802) = √3600 = 60 m.

  3. Moving 60 m west (the south-west leg's x-component) from the mall's x = 250 gives the college's x-coordinate: 250 − 60 = 190. So the college is at (190, 0).

Distance calculation

  1. Δx between Axis Bank (110, 150) and College (190, 0): 190 − 110 = 80 m.

  2. Δy between the two points: 150 − 0 = 150 m.

  3. Shortest distance = √(802 + 1502) = √(6400 + 22500) = √28900 = 170 m.

Cross-check: 80–150–170 is a scaled 8–15–17 Pythagorean triple (×10), confirming the arithmetic. Plugging the college's coordinates back into the final leg — Δx = 60 m, Δy = 80 m from the mall — gives √(602 + 802) = √(3600 + 6400) = √10000 = 100 m, exactly matching the stated south-west walk, so the derived coordinates are internally consistent.

Hence, the shortest distance between Axis Bank and the college is 170 m.

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