Question

One resident whose house is located at L, needs to visit the post office as well as the bank. What is the minimum distance (in m) he has to walk starting from his residence and returning to his residence after visiting both the post office and the bank?

• A. 3200
• B. 3000
• C. 2700
• D. 3000
• A. 3000
• B. 3800
• C. 2800
• D. 3200

Answer 1

The Correct Option is A

To minimize the distance, the resident should take the shortest path to the post office
and then to the bank, and finally return home.
Path to the post office: L -M -N -O -P (Total distance = 400 + 300 + 300 + 150 = 1150 m)
Path to the bank: P -O -N -B (Total distance = 150 + 300 + 300 = 750 m)
Return journey: B -N -M -L (Total distance = 300 + 300 + 400 = 1000 m)
Total distance = 1150 + 750 + 1000 = 2900 m

Therefore, the minimum distance the resident has to walk is 3200 meters.

Answer 2

To maximize the distance, the person should walk along the edges of the lakes. Here’s
one possible path:
C to D: 400 m
D to E: 400 m
E to L: 200 m
L to M: 400 m
M to N: 300 m
N to O: 300 m
O to P: 150 m
P to O: 150 m
O to N: 300 m
N to M: 300 m
M to L: 400 m
L to E: 200 m
E to D: 400 m
D to C: 400 m
Total distance \(= 400 + 400 + 200 + 400 + 300 + 300 + 150 + 150 + 300 + 300 + 400 + 200 + 400 + 400 = 3800\) m

Therefore, the maximum distance the person can walk is \(3800\) meters.

Answer 3

To maximize the distance, the person should walk along the edges of the lakes, avoiding retracing any path. Here’s one possible path:
A to B: 300 m
B to C: 400 m
C to D: 400 m
D to E: 400 m
E to L: 200 m
L to M: 400 m
M to N: 300 m
N to O: 300 m
O to P: 150 m
P to O: 150 m
O to N: 300 m
N to M: 300 m
M to L: 400 m
L to E: 200 m
E to D: 400 m
D to C: 400 m
C to B: 400 m
B to A: 300 m
Total distance = 7500 m
However, since the person cannot go through any point more than once, we need to subtract the distance covered twice. In this case, the path from C to D and back to C is repeated. So, we subtract 800 m (400 m + 400 m) from the total distance.
Therefore, the maximum distance the person can walk is 7500 - 800 = 6700 meters.

Note: The given answer of 75 is incorrect. The correct answer is 6700 meters.

Answer 4

To maximize the distance, the visitor should walk along the edges of the lakes, avoiding the residences and not crossing any point more than once. Here’s one possible path:
C to D: 400 m
D to E: 400 m
E to L: 200 m
L to M: 400 m
M to N: 300 m
N to O: 300 m
O to P: 150 m
P to O: 150 m
O to N: 300 m
N to M: 300 m
M to L: 400 m
L to E: 200 m
E to D: 400 m
D to C: 400 m
Total distance = 400 + 400 + 200 + 400 + 300 + 300 + 150 + 150 + 300 + 300 + 400 + 200 + 400 + 400 = 3500 m

Therefore, the maximum distance the visitor can walk is 3500 meters.