Logical Reasoning Discussion

**Common Information**

1200 vehicles travel every day from Point $A$ to Point $Z$ on a network of one-way roads as shown in the diagram below.

Points $B$, $C$, $M$, $D$ and $E$ are junctions in this network. The number adjacent to the ray depicting each road stands for the cost (in rupees) of travelling on that road. Each vehicle takes the path of least cost from $A$ to $Z$.

If two or more paths have the same cost, then the vehicles are distributed equally on those paths.

Q. |
Which junctions together have the maximum traffic each day? |

✖ A. |
B and C |

✖ B. |
D and E |

✖ C. |
D and M |

✔ D. |
M and E |

✖ E. |
B and E |

**Solution:**

Option(**D**) is correct

Let us analyze the given information.

Here the roads have associated costs, but the nodes do not have associated costs.

From the diagram, observe that the possible routes from $A$ (the initial point) to $Z$ (the final point) are:

$A – B – C – Z$, $A – M – Z$, $A – M – E – Z$ and $A – D – E – Z$.

Let us tabulate the total costs incurred in travelling along each path.

Table below can be scrolled horizontally

Route | Cost (in rupees) |
---|---|

$A – B – C – Z$ | $3 + 5 + 5$ $= 13$ |

$A – M – Z$ | $4 + 7$ $= 11$ |

$A – M – E – Z$ | $4 + 4 + 2$ $= 10$ |

$A – D – E – Z$ | $6 + 7 + 2$ $= 15$ |

Since all the vehicles on any given day travel along the path having the least cost, they would travel along the path $A-M-E-Z$. The two junctions on this route are $M$ and $E$. Thus, $M$ and $E$ together have the maximum traffic each day.

Hence, **option D** is the correct choice.