Dev, Kumar, Nilesh, Ankur, and Pintu are standing facing North in a…
2023
Dev, Kumar, Nilesh, Ankur, and Pintu are standing facing North in a playground, positioned as follows: Kumar is 40 m to the right of Ankur. Dev is 60 m to the south of Kumar. Nilesh is 25 m to the west of Ankur. Pintu is 90 m to the north of Dev. If a boy starts from Nilesh, walks to Ankur, then to Kumar, then to Dev, and finally to Pintu, walking in a straight line for each leg, what is the total distance he covered?
- A.
215 m
- B.
155 m
- C.
245 m
- D.
185 m
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept: In a direction-sense problem, each stated relation ("right of"/east, "south of", "west of", "north of", with everyone facing North) fixes a straight segment lying along one of the four cardinal directions between two named points. Depending on the two directions involved, consecutive segments on a path can be collinear (lying on the same east-west or north-south line, possibly in opposite ways) or perpendicular to each other; either way, the total distance walked along a stated multi-leg path is simply the sum of each leg's given length, taken in the order walked.
Application: Placing Ankur at the origin and taking East/North as positive axes, each statement fixes one leg of the walk:
Nilesh to Ankur: Nilesh is 25 m west of Ankur, so walking from Nilesh to Ankur covers 25 m.
Ankur to Kumar: Kumar is 40 m to the right of Ankur (East, since both face North), so this leg covers 40 m.
Kumar to Dev: Dev is 60 m to the south of Kumar, so this leg covers 60 m.
Dev to Pintu: Pintu is 90 m to the north of Dev, so this leg covers 90 m.
Adding the four legs in the order walked: 25 + 40 + 60 + 90 = 215 m.
Cross-check: Place Ankur at the reference point (0 m east, 0 m north). Then Kumar is 40 m east of Ankur, Nilesh is 25 m west of Ankur (i.e., at -25 m east), Dev is 60 m south of Kumar (40 m east, -60 m north), and Pintu is 90 m north of Dev (40 m east, 30 m north). Walking Nilesh to Ankur covers the 25 m gap along the east-west line; Ankur to Kumar covers the 40 m gap along that same line; Kumar to Dev covers the 60 m drop along the north-south line through Kumar; and Dev to Pintu covers the 90 m rise along that same line. These four legs again total 25 + 40 + 60 + 90 = 215 m, confirming the answer independently.