Read the given information carefully and answer the questions given beside:…
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Read the given information carefully and answer the questions given beside:
Ramlin and Divya are two friends. They start walking from same point but in opposite direction. Ramlin walks towards north. After walking 10km Ramlin takes a right turn and walks for 5km then turns 90 degree in clockwise direction and walks 20km to reach his office and then takes a left turn and walks 5km to reach canteen. Divya also follows the same condition as Ramlin.
If Ramlin takes another left turn from canteen and walks 20km to reach his home.
Then find the shortest distance between Ramlin’s homes to Ramlin’s office?
- A.
9√12 km
- B.
4√37 km
- C.
5√17 km
- D.
17√5 km
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Key idea: place the starting point at (0,0) and track Ramlin's moves using coordinates.
Ramlin walks north 10 km: position (0, 10).
He then turns right (east) and walks 5 km: position (5, 10).
He turns 90° clockwise (now facing south) and walks 20 km to reach his office: position (5, -10).
From the office he turns left (east) and walks 5 km to the canteen: position (10, -10).
From the canteen he takes another left (north) and walks 20 km to reach his home: position (10, 10).
Now compute the shortest distance between Ramlin's home (10, 10) and his office (5, -10).
Horizontal difference: Δx = 10 - 5 = 5 km.
Vertical difference: Δy = 10 - (−10) = 20 km.
Distance = sqrt(Δx^2 + Δy^2) = sqrt(5^2 + 20^2) = sqrt(25 + 400) = sqrt(425) = 5√17 km.
Therefore, the shortest distance between Ramlin’s home and Ramlin’s office is 5√17 km.