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Speed, Distance and Time: Route Timings

XAT 2016 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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Study the figure below and answer the question:

(Figure shows points A, B, C, D with routes ABCD, ABD, ACD, ACBD)

Four persons walk from Point A to Point D following different routes. The one following ABCD takes 70 minutes. Another person takes 45 minutes following ABD. The third person takes 30 minutes following route ACD. The last person takes 65 minutes following route ACBD. If all were to walk at the same speed, how long will it take to go from point B to point C?

  1. A.

    10 min.

  2. B.

    20 min.

  3. C.

    30 min.

  4. D.

    40 min.

  5. E.

    Cannot be answered as the angles are unknown.

Answer

C

Explanation

Let time for segment XYXY be t(XY)t(XY).

  1. t(AB)+t(BC)+t(CD)=70t(AB) + t(BC) + t(CD) = 70
  2. t(AB)+t(BD)=45t(AB) + t(BD) = 45
  3. t(AC)+t(CD)=30t(AC) + t(CD) = 30
  4. t(AC)+t(BC)+t(BD)=65t(AC) + t(BC) + t(BD) = 65

Add (1) and (4): t(AB)+t(AC)+2t(BC)+t(CD)+t(BD)=135t(AB) + t(AC) + 2 t(BC) + t(CD) + t(BD) = 135 Substitute (2) and (3): 45+30+2t(BC)=135  ⟹  2t(BC)=60  ⟹  t(BC)=30 min.45 + 30 + 2 t(BC) = 135 \implies 2 t(BC) = 60 \implies t(BC) = 30 \text{ min.}

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