What was the total duration of calls (in minutes) made by Kabir to friends on the Vertex network?
Answer and solution
Correct answer: 525
Solution
Answer: 525
1. Calls received from AeroNet by Vertex users total 250+275+100+100=725 minutes.
2. They are made by Kabir or Zoya, the only AeroNet users. Zoya contributes 200 minutes.
3. Kabir therefore contributes 725−200=525 minutes. This is network-flow conservation, not equality of an individual’s outgoing and incoming calls.
Detailed setup and verification:
Write the relevant four destination cells before subtracting anything: Rahul 250, Priya275, Vikram100 and Ananya100 incoming minutes from AeroNet. These count the same calls as the two AeroNet users’ outgoing-to-Vertex cells, just from the receivers’ side. Each minute is counted once on each side.
Thus Kabir + Zoya =725. Zoya’s 200 is given, so Kabir = 525. Verification:525+200=725. Do not use Kabir’s 225 incoming from Vertex: that is the reverse direction and is a separate collection of calls.
Verification: 3. Kabir therefore contributes 725−200=525 minutes. This is network-flow conservation, not equality of an individual’s outgoing and incoming calls.
Trap to avoid: Balance only AeroNet→Vertex calls.
1. Calls received from AeroNet by Vertex users total 250+275+100+100=725 minutes.
2. They are made by Kabir or Zoya, the only AeroNet users. Zoya contributes 200 minutes.
3. Kabir therefore contributes 725−200=525 minutes. This is network-flow conservation, not equality of an individual’s outgoing and incoming calls.
Detailed setup and verification:
Write the relevant four destination cells before subtracting anything: Rahul 250, Priya275, Vikram100 and Ananya100 incoming minutes from AeroNet. These count the same calls as the two AeroNet users’ outgoing-to-Vertex cells, just from the receivers’ side. Each minute is counted once on each side.
Thus Kabir + Zoya =725. Zoya’s 200 is given, so Kabir = 525. Verification:525+200=725. Do not use Kabir’s 225 incoming from Vertex: that is the reverse direction and is a separate collection of calls.
G Strategy shortcut
Method: Cross-network total 725 minus Zoya 200 gives Kabir 525.Verification: 3. Kabir therefore contributes 725−200=525 minutes. This is network-flow conservation, not equality of an individual’s outgoing and incoming calls.
Trap to avoid: Balance only AeroNet→Vertex calls.
G Strategy: Method: Cross-network total 725 minus Zoya 200 gives Kabir 525. Verification: 3. Kabir therefore contributes 725−200=525 minutes. This is network-flow conservation, not equality of an individual’s outgoing and incoming calls. Trap to avoid: Balance only AeroNet→Vertex calls.