Logical Reasoning Discussion

**Common Information**

There are seven cities P, Q, R, S, T, U, and V. The table below shows all the possible direct routes to and fro between any two of the cities. It also gives both the Air as well as the Land route distances (in miles) between those cities and the time required (in hrs) for the respective journeys. A person on any one of the above seven places can travel to any one of the remaining 6 places using Air or Land route only. The person can change his/her mode of transport (Air/Land) at any of the above seven places.

Table below can be scrolled horizontally

Direct Routes |
Air Distance (in miles) |
Air Time (in hrs) |
Land Distance (in miles) |
Land Time (in hrs) |
---|---|---|---|---|

P – Q | 1100 | 3 | 900 | 6 |

P – S | 2200 | 6 | 2400 | 10 |

P – R | 700 | 2 | 1000 | 6 |

Q – U | 1800 | 5 | 2200 | 11 |

Q – T | 800 | 3 | 1100 | 6 |

R – T | 1000 | 3 | 1400 | 10 |

S – T | 800 | 3 | 1000 | 5 |

S – V | 2200 | 6 | 2800 | 14 |

T – V | 2200 | 6 | 3000 | 15 |

U – V | 800 | 4 | 1200 | 6 |

Q. |
If Mr. X wants to go from P to V in the minimum time possible, then which of the following routes should be preferred? |

✔ A. |
PQUV by Air |

✖ B. |
PSTV by Air |

✖ C. |
PQUV by Land |

✖ D. |
PQTSV by Land |

✖ E. |
PSTV by Land |

**Solution:**

Option(**A**) is correct

The time for the given routes can be calculated as follows:

PQUV by Air = PQ + QU + UV = 3 + 5 + 4 = 12 hrs

PSTV by Air = PS + ST + TV = 6 + 3 + 6 = 15 hrs

PQUV by Land = PQ + QU + UV = 6 + 11 + 6 = 23 hrs

PQTSV by Land = PQ + QT + TS + SV = 6 + 6 + 5 + 14 = 31 hrs

PSTV by Land = PS + ST + TV = 10 + 5 + 15 = 30 hrs

Hence, travelling from P to V through the route PQUV by air takes the minimum time.

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