Direction: Read the given information carefully and answer the questions given…
Direction: Read the given information carefully and answer the questions given below (a set of 2 questions). Kishore and Lokesh are siblings and live in the same room. Both of them go to their respective colleges by different routes. The colleges of both Kishore and Lokesh are in the east direction with respect to their room. Kishore moves 150 m in the north direction and turns right. After walking 110 m, he reaches Axis Bank. He then turns right and moves 70 m to reach a traffic signal. He then turns left and moves 140 m to reach the shopping mall. Finally, he moves 100 m in the south-west direction to reach his college. What is the shortest distance between Axis Bank and his college? [Questions 8 and 9 are linked together.]
Answer: C. 170 m — Concept: In direction-sense problems, fix East as +x and North as +y and track each turn with the rule that a right turn rotates the current heading 90…
- A.
150 m
- B.
160 m
- C.
170 m
- D.
180 m
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept: In direction-sense problems, fix East as +x and North as +y and track each turn with the rule that a right turn rotates the current heading 90 degrees clockwise (N -> E -> S -> W -> N) while a left turn rotates it 90 degrees counter-clockwise. Once every point on the path has coordinates, the shortest (straight-line) distance between any two of those points is the Euclidean distance given by the Pythagorean theorem: distance = square root of (delta-x squared + delta-y squared).
Place the room at the origin (0, 0). Kishore walks 150 m north, so he is now at (0, 150).
Facing north, he turns right, so he now faces east; walking 110 m east puts Axis Bank at (110, 150).
Facing east, he turns right, so he now faces south; walking 70 m south puts the traffic signal at (110, 80).
Facing south, he turns left, so he now faces east; walking 140 m east puts the shopping mall at (250, 80).
From the mall he walks 100 m south-west to the college. Since the college must lie exactly east of the room (same y as the room, per the passage's own clue), the southward part of this 100 m move must cancel the mall's y = 80, so the south component is 80 m; the remaining west component follows from 100 squared = 80 squared + west squared, giving west = square root of (10000 - 6400) = 60 m. So the college sits at (250 - 60, 80 - 80) = (190, 0).
Axis Bank is at (110, 150) and the college is at (190, 0). The shortest distance between them is the square root of ((190-110) squared + (150-0) squared) = square root of (80 squared + 150 squared) = square root of (6400 + 22500) = square root of 28900 = 170 m.
Cross-check: The 80-60-100 triangle used for the final south-west leg and the 80-150-170 triangle used for the answer are both familiar scaled Pythagorean triples (3-4-5 x 20 and 8-15-17 x 10), which confirms the arithmetic is clean. Independently, the resulting college position (190, 0) has the same y-coordinate as the room, exactly matching the passage's stated constraint that the college lies due east of the room -- a consistent check on the whole path.
Result: The shortest distance between Axis Bank and Kishore's college is 170 m.