GATE CSE 2020 | Question: GA-5

Question

There are multiple routes to reach from node $1$ to node $2$, as shown in the network.

The cost of travel on an edge between two nodes is given in rupees. Nodes $\text{‘}a\text{’}, \text{‘}b\text{’}, \text{‘}c\text{’}, \text{‘}d\text{’}, \text{‘}e\text{’},$ and $\text{‘}f\text{’}$ are toll booths. The toll price at toll booths marked $\text{‘}a\text{’}$ and $\text{‘}e\text{’}$ is Rs. $200$, and is Rs. $100$ for the other toll booths. Which is the cheapest route from node $1$ to node $2$?

• A. $1-a-c-2$
• B. $1-f-b-2$
• C. $1-b-2$
• D. $1-f-e-2$

Comments

b. 1-f-b-2

Answer 1

$A) 1-a-c-2 :$

• $1-a = 200$
• Tax at $a =200$
• $a-c = 100$
• Tax at $c = 100$
• $c-2 : 100$
• Total $= 200+200+100+100+100 = 700$

$B) 1-f-b-2 :$

• $1-f = 100$
• Tax at $f =100$
• $f-b = 0$
• Tax at $b = 100$
• $b-2 : 200$
• Total $= 100+100+0+100+200 = 500$

$C) 1-b-2 :$

• $1-b = 300$
• Tax at $b = 100$
• $b-2 : 200$
• Total $= 300+100+200 = 600$

$D) 1-f-e-2 :$

• $1-f = 100$
• Tax at $f =100$
• $f-e = 100$
• Tax at $e = 200$
• $e-2 : 200$
• Total $= 100+100+100+200+200 = 700$

Cheapest route $= 1-f-b-2$

Correct Option: B

Comments

@Shaik Masthan 

Bro this question was in 1 marks, right?

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Some people may have forgotten to add toll of rs 100 or 200 on respective toll booths and considering only path cost, but still, the answer will be same.