Low-cost airline routes and pricing

CAT 2007 Slot 1 · DILR · Hard · Data Interpretation

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Passage / data set

A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company. Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports.

Sector NoAirport of DepartureAirport of ArrivalDistance (km)Price (Rs.)
1AB560670
2AC7901350
3AD8501250
4AE12451600
5AF13451700
6AG13502450
7AH19501850
8BC16502000
9BH17501900
10BI21002450
11BJ23002275
12CD460450
13CF410430
14CG9101100
15DE540590
16DF625700
17DG640750
18DH9501250
19DJ16502450
20EF12501700
21EG9701150
22EH850875
23FG9001050
24FI875950
25FJ9701150
26GI510550
27GJ830890
28HI790970
29HJ400425
30IJ460540

Question 1 of 5

What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J?

  1. A.

    2275

  2. B.

    2850

  3. C.

    2890

  4. D.

    2930

  5. E.

    3340

Answer

D

Explanation

Shortest route by distance from A to J: Path A-C-F-J: distance =790+410+970=2170= 790 + 410 + 970 = 2170 km. Price =1350+430+1150=2930= 1350 + 430 + 1150 = 2930 Rs.

Question 2 of 5

The company plans to introduce a direct flight between A and J. The market research results indicate that all its existing passengers travelling between A and J will use this direct flight if it is priced 5% below the minimum price that they pay at present. What should the company charge approximately, in rupees, for this direct flight?

  1. A.

    1991

  2. B.

    2161

  3. C.

    2707

  4. D.

    2745

  5. E.

    2783

Answer

B

Explanation

Cheapest route overall from A to J is A-H-J: Price =1850+425=2275= 1850 + 425 = 2275 Rs. Direct flight price =0.95×2275=2161.25≈2161= 0.95 \times 2275 = 2161.25 \approx 2161 Rs.

Question 3 of 5

If the airports C, D and H are closed down owing to security reasons, then what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J?

  1. A.

    2275

  2. B.

    2615

  3. C.

    2850

  4. D.

    2945

  5. E.

    3190

Answer

C

Explanation

If C, D, H are closed, valid paths from A to J are:

  • A-F-J: Price =1700+1150=2850= 1700 + 1150 = 2850 Rs.
  • A-G-J: Price =2450+890=3340= 2450 + 890 = 3340 Rs. Minimum price is Rs. 2850.

Question 4 of 5

If the prices include a margin of 10% over the total cost that the company incurs, then what is the minimum cost per kilometer that the company incurs in flying from A to J?

  1. A.

    0.77

  2. B.

    0.88

  3. C.

    0.99

  4. D.

    1.06

  5. E.

    1.08

Answer

B

Explanation

Cost per km =Price1.10×Distance= \frac{\text{Price}}{1.10 \times \text{Distance}}. For path A-H-J: Price =2275= 2275, Distance =1950+400=2350= 1950 + 400 = 2350 km. Cost per km =22751.10×2350=22752585≈0.88= \frac{2275}{1.10 \times 2350} = \frac{2275}{2585} \approx 0.88.

Question 5 of 5

If the prices include a margin of 15% over the total cost that the company incurs, then which among the following is the distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company?

  1. A.

    2170

  2. B.

    2180

  3. C.

    2315

  4. D.

    2350

  5. E.

    2390

Answer

D

Explanation

Minimizing cost per kilometer is equivalent to minimizing PriceDistance\frac{\text{Price}}{\text{Distance}}. For path A-H-J, distance =2350= 2350 km, price =2275= 2275. Ratio 22752350≈0.968\frac{2275}{2350} \approx 0.968, which is the minimum.

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