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In a directed weighted graph, if the weight of every edge is decreased by 10 units, does any change occur to the shortest path in the modified graph?

(a) 209

(b) 65

(c) 57

(d) 43

This question was addressed to me in an interview.

My question is based upon Different Path in a Graph topic in section Graphs of Discrete Mathematics

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Right answer is (c) 57

To explain: The shortest path will change in the modified graph. Suppose that the shortest path is of weight 21 and has 7 edges and there is another path with 4 edges and total weight 17. Now, the weight of the first shortest path is increased by 7*10 and becomes 21 + 70 and the weight of the second path is increased by 4*10 and becomes 17 + 40. So the shortest path changes to the other path with weight as 57.

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