Question

Shyam's house, his office and his gym are all equidistant from each other. The distance between any 2 of them is 4 km. Shyam starts walking from his gym in a direction parallel to the road connecting his office and his house and stops when he reaches a point directly east of his office. He then reverses direction and walks till he reaches a point directly south of his office. The total distance walked by Shyam is

• A. 9 km
• B. 6 km
• C. 16 km
• D. 12 km

Answer 1

The Correct Option is D

To solve this problem, we need to visualize the positions of Shyam's house, office, and gym. Since these points are equidistant, they form an equilateral triangle with each side measuring 4 km. Let's denote the gym as G, the office as O, and the house as H. The positions can be laid out as follows: imagine placing point O at the origin (0, 0) of a coordinate plane, H at (4, 0), and G at (2, √12) because G should be 4 km from both O and H, forming a triangle. The coordinates of O, H, and G ensure they are equidistant.

1. Shyam starts walking parallel to OH, eastwards from G. As G is directly above the midpoint of OH, heading east will take Shyam along a parallel path to OH.

2. Since G is at (2, √12), walking east until he is directly east of O means he reaches x-coordinate (√12). The distance walked in this path is `√12 - 2`.

3. Now, from this point, he reverses direction and walks south directly until he aligns south to O. Since he reaches a point horizontally aligned to O, this means he is at (√12, 0). The vertical path from (2, √12) directly down to x-axis is also √12.

4. The total distance walked: First eastwards: `2 km`, then south: `4 km`, resulting in `4 km` south and `2 + 2 = 4 km` east. Therefore, the total distance is `8 km`.

Total Distance = 8 km

Hence, the correct calculation reflects that the total distance walked by Shyam is 8 km, not 12 km as mentioned in the correct answer.