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 the air route and the land route fares are $\$$35 and $\$$25 respectively per 100 miles for a passenger, which is the cheapest route from Q to S via R? |

✖ A. |
QTRPS by Land |

✖ B. |
QPRTS by Air |

✔ C. |
QPRTS by Land |

✖ D. |
Both (A) and (B) |

✖ E. |
None of these |

**Solution:**

Option(**C**) is correct

Total fare = Route distance $\times$ Fare per mile

∴ The fares for the given routes can be calculated as follows:

QPRTS by Air $= (1100 + 700 + 1000 + 800) \times \dfrac{35}{100}$ $= \$ 1260$

QPRTS by Land $= (900 + 1000 + 1400 + 1000) \times \dfrac{25}{100}$ $= \$ 1075$

QTRPS by Land $= (1100 + 1400 + 1000 + 2400) \times \dfrac{25}{100}$ $= \$ 1475$

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