Consider the following diagram (not in scale) :
[Diagram showing points P, Q, R, S, T, U and V with connecting lines and distances]
There are seven places marked as P, Q, R, S, T, U and V as shown in the diagram. The directly connected paths between two places are indicated by line segments joining the two places along with the length labelled in km. Then, the shortest distance between P and U is:
14 km
15 km
12 km
13 km
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2016
Paths from P to U:
1. Direct path via T: P -> T -> U. The length is P-T (6 km) + T-U (9 km) = 15 km.
2. Paths via V: First, find the shortest path from P to V.
– P -> Q -> V: 4 km + 8 km = 12 km
– P -> R -> V: 5 km + 8 km = 13 km
– P -> S -> V: 6 km + 8 km = 14 km
– P -> R -> S -> V: 5 km + 2 km + 8 km = 15 km
– P -> Q -> R -> V: 4 km + 3 km + 8 km = 15 km
The shortest path from P to V is 12 km (P-Q-V). The path from V to U is 4 km.
So, the shortest path via V is P -> V -> U = 12 km + 4 km = 16 km.
Comparing the shortest path via T (15 km) and the shortest path via V (16 km), the minimum distance is 15 km.