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Road Network Travel Time Optimization

XAT 2025 · Quantitative Ability & Data Interpretation · Hard · Speed Distance Time

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Passage / data set

The diagram depicts a road network connecting five towns, namely Meereen, Lannisport, Winterfell, Oldtown, and Gulltown. The maximum speed limits along any stretch of road are as shown:

  • Meereen to Oldtown: 100 km/hr
  • Oldtown to Gulltown: 25 km/hr
  • Gulltown to Winterfell: 120 km/hr
  • Oldtown to Lannisport: 20 km/hr
  • Meereen to Lannisport to Winterfell: 120 km/hr

It takes 1 hour to reach Oldtown from Meereen (Distance = 100 km), 2 hours to reach Gulltown from Oldtown (Distance = 50 km), and 45 minutes to reach Winterfell from Gulltown (Distance = 90 km).

Question 1 of 3

Tyrion Lannister drove from Meereen to Oldtown, then from Oldtown to Lannisport, and finally from Lannisport to Winterfell, always taking the shortest paths. He always drove at a speed 10 km/hr below the maximum speed limits for the stretches he took. What was his total driving time closest to?

  1. A.

    3 hrs 19 mins

  2. B.

    4 hrs 20 mins

  3. C.

    7 hrs 28 mins

  4. D.

    6 hrs 42 mins

  5. E.

    7 hrs 50 mins

Answer

C

Explanation

Distances: Meereen to Oldtown = 100 km. Reduced speed = 100−10=90100 - 10 = 90 km/hr. Time = 100/90=1.111100/90 = 1.111 hr. Oldtown to Lannisport = 60 km. Reduced speed = 20−10=1020 - 10 = 10 km/hr. Time = 60/10=660/10 = 6 hr. Lannisport to Winterfell = 40 km. Reduced speed = 120−10=110120 - 10 = 110 km/hr. Time = 40/110=0.363640/110 = 0.3636 hr. Total time = 1.111+6+0.3636=7.4751.111 + 6 + 0.3636 = 7.475 hrs = 7 hrs 28.5 mins.

Question 2 of 3

Missandei starts from Gulltown towards Oldtown by the shortest path, driving at the maximum permissible speed. From Oldtown, she drives at a speed of 10 km/hr towards Lannisport. When Missandei starts from Gulltown, Varys starts at the same time from Lannisport to Oldtown along the shortest path, always driving at the maximum permissible speed. If they don't stop anywhere, at what point will they meet?

  1. A.

    Approximately 13.33 km south of Oldtown.

  2. B.

    Approximately 54.33 km north of Lannisport.

  3. C.

    Approximately 57.33 km north of Lannisport.

  4. D.

    Approximately 6.67 km south of Oldtown.

  5. E.

    Cannot be uniquely determined from the given information.

Answer

D

Explanation

Missandei: Gulltown to Oldtown (50 km at 25 km/hr) takes 2 hours. In 2 hours, Varys travels from Lannisport towards Oldtown at 20 km/hr   ⟹  20×2=40\implies 20 \times 2 = 40 km. At t=2t = 2 hours, Missandei is at Oldtown, Varys is 40 km north of Lannisport (20 km south of Oldtown). They now travel towards each other on the 20 km stretch between Oldtown and Varys's position: Relative speed = 10+20=3010 + 20 = 30 km/hr. Time to meet = 20/30=2/320 / 30 = 2/3 hour. Distance Missandei travels from Oldtown = 10×(2/3)=6.6710 \times (2/3) = 6.67 km. So they meet 6.67 km south of Oldtown.

Question 3 of 3

The capital city, King's Landing, located 40 km to the south of Gulltown on the road connecting Gulltown to Winterfell, did not have a straight road connecting to Meereen. Now, a new expressway is being built to connect these two towns by a straight road. What should be the maximum speed limit allowed on this expressway so that it cuts down the travel time, from Meereen to King's Landing, from the fastest possible route through the road network shown in the diagram, by 20 minutes?

  1. A.

    100 km/hr

  2. B.

    130 km/hr

  3. C.

    139 km/hr

  4. D.

    120 km/hr

  5. E.

    157 km/hr

Answer

D

Explanation

Fastest route from Meereen to King's Landing currently: Path MWK: Meereen to Winterfell (120 km at 120 km/hr = 1 hr) + Winterfell to King's Landing (50 km at 120 km/hr = 25 mins) = 1 hr 25 mins = 85 mins. If expressway cuts time by 20 mins, new travel time = 65 mins = 13/1213/12 hours. Direct distance from Meereen to King's Landing = 1202+502=130\sqrt{120^2 + 50^2} = 130 km. Required Speed = 130/(13/12)=120130 / (13/12) = 120 km/hr.

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