A Postman walked 7 kms. North from the post office to reach Mr. Singh’s house. He took a left turn and walked 4kms. To reach Mr. kumar’s house. he then took a right turn and walk 3kms. To reach Mr Sharma house the distance between Mr Sharma and Mr. Singh’s house is

The correct answer is A. Place the post office at the origin. The postman walks 7 km north to Mr. Singh's house, so Singh is at (0, 7). Facing north, a left turn means heading west. Walking 4 km west takes him to Mr. Kumar's house at (-4, 7). A right turn from west means heading north, and 3 km more brings him to Mr. Sharma's house at (-4, 10).

The distance between Sharma and Singh is the straight line joining them, which forms a right-angled triangle with legs of 4 km (east-west) and 3 km (north-south). By Pythagoras, the hypotenuse is √(16+9) = 5 km. This is a direction-and-distance problem of the kind reasoning sections test repeatedly, and the same coordinate method works for every such question.

• Option B (6 km) and Option D (7 km) ignore the geometry of the turns and simply add or repeat legs of the path.
• Option C (4 km) takes only the westward leg, which is the distance from Kumar's house to Singh's house, not Sharma's.

Trap: adding 4 + 3 = 7 km, or stopping at the total distance walked, instead of finding the straight-line displacement. Always sketch the path and join the start and end points.