Logical Reasoning Discussion

**Common Information**

The flow of energy from Generator (G) to Motor (M) in a power distribution network is as shown. Points P, Q, R and S are capacitor banks (denoted by CB) in the network. The arrows mark the direction of the energy flow. The energy loss (in Rs. ’00) in the power lines during the flow is indicated by the numbers adjacent to the arrows.

An energy analyst has to make sure that when the energy flows from G to M, it flows through a path where the total energy loss (in Rs. ’00) is minimal. There is an additional energy loss (in Rs. ’00) at the capacitor banks. This loss can be regulated. For example, if the energy analyst selects a path G – P – M (using CB P) then the total energy loss would be Rs. 1,000 + Rs. 600 + the regulated energy loss at the CB P.

Q. |
If the energy analyst wants to ensure that the energy loss from G to M across all the paths is same, then a feasible set of regulated energy losses (in Rs. ’00) at the capacitor banks P, Q, R and S respectively to achieve this goal is: |

✖ A. |
4, 0, 2, 1 |

✖ B. |
1, 4, 0, 2 |

✖ C. |
0, 5, 1, 3 |

✔ D. |
0, 4, 2, 1 |

✖ E. |
None of these |

**Solution:**

Option(**D**) is correct

Let us analyze the given information.

Let us assume that the energy losses (in Rs. ’00) at the capacitor banks P, Q, R and S are *p*, *q*, *r* and *s *respectively.

Draw a table showing the energy losses (in Rs. ’00) for all possible routes between G and M in terms of the variables above.

Table below can be scrolled horizontally

Route | Energy loss(in Rs. ’00) |
---|---|

G – P – M | 10 + p + 6 = 16 + p |

G – Q – P – M | 3 + q + 3 + p + 6 = 12 + q + p |

G – Q – R – M | 3 + q + 4 + r + 3 = 10 + q + r |

G – S – M | 8 + s + 7 = 15 + s |

G – S – R – M | 8 + s + 2 + r + 3 = 13 + s + r |

The total energy loss across all paths should be the same. This implies that the values of the variables *p*, *q*, *r* and *s* should be such that the 5 sums given above should be equal. This can be found either by solving the equations for the energy loss on each route or by substituting the value of the variables from each answer option and checking for equality. Here, the values are found by solving the equations.

Equating the energy losses on the first two paths, we get,

16 + *p* = 12 + *q* + *p*

∴ *q* = 4

Equating the energy losses on the third and fifth paths, we get,

10 + *q* + *r* = 13 + *s* + *r*

∴ *s* = 1

Equating the energy losses on the first and fourth paths, we get,

16 + *p* = 15 + *s*

∴ *p* = 0

Equating the energy losses on the second and third paths we get,

12 + *q* + *p* = 10 + *q* + *r*

∴ *r* = 2

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