R walks a long distance every Sunday. He walks 2 km towards the north from his house and then turns right; he walks another 2 km and again turns right; next he walks 5 km and turns left; he further walks 2 km and stops. He rests for some time and returns home following a straight route without any turning point. What is the distance R walks after he has rested ?
11 km
7 km
6 km
5 km
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2020
– 1. Walks 2 km towards North: Reaches point (0, 2).
– 2. Turns right (East) and walks 2 km: Reaches point (0+2, 2) = (2, 2).
– 3. Turns right (South) and walks 5 km: Reaches point (2, 2-5) = (2, -3).
– 4. Turns left (East) and walks 2 km: Reaches point (2+2, -3) = (4, -3).
– R stops at the point (4, -3). This point is 4 km East and 3 km South of his house (0,0).
– He returns home following a straight route from (4, -3) to (0,0).
– This is the distance between these two points, which can be calculated using the distance formula or by recognizing it as the hypotenuse of a right triangle with legs of length 4 km and 3 km.
– Distance = $\sqrt{(4-0)^2 + (-3-0)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$ km.
– The distance R walks after he has rested is the length of this straight return journey, which is 5 km.