Direction TestMTP Sep 24 Series IIQuestion 2330 of 165
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Seven villages A, B, C, D, E, F and G are situated as follows: E is 2\displaystyle 2 km to the west of B F is 2\displaystyle 2 km to the north of A C is 1\displaystyle 1 km to the west of A D is 2\displaystyle 2 km to the south of G G is 2\displaystyle 2 km to the east of C D is exactly in the middle of B and E. Which two villages are the farthest from one another?

Options

AF and E
BD and C
CF and B
DG and E
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Correct Answer

✅ Option c — F and B

All Options:

  • AF and E
  • BD and C
  • CF and B
  • DG and E

Detailed Solution & Explanation

Let A be at (0,0)\displaystyle (0,0):
- F is 2 km North   ⟹  F=(0,2)\displaystyle \implies F = (0, 2).
- C is 1 km West   ⟹  C=(−1,0)\displaystyle \implies C = (-1, 0).
- G is 2 km East of C   ⟹  G=(1,0)\displaystyle \implies G = (1, 0).
- D is 2 km South of G   ⟹  D=(1,−2)\displaystyle \implies D = (1, -2).
Since D is the midpoint between B and E, and E is 2 km West of B, we have:
- E=(0,−2)\displaystyle E = (0, -2) (1 km West of D).
- B=(2,−2)\displaystyle B = (2, -2) (1 km East of D).
Let us calculate the distance between F (0,2)\displaystyle (0,2) and B (2,−2)\displaystyle (2,-2):
DistanceFB=22+(−2−2)2=4+16=20≈4.47 km\text{Distance}_{FB} = \sqrt{2^2 + (-2 - 2)^2} = \sqrt{4 + 16} = \sqrt{20} \approx 4.47\text{ km}
Comparing all pairwise distances, F and B are the farthest from one another.
Hence, **Option C** is the correct answer.

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