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Discussion :: Time and Distance

  1. The towns A, B and C are on a straight line. Town C is between A and B. The distance from A to B is 100 km. How far is A from C?

    I. 

    The distance from A to B is 25% more than the distance from C to B.

     II. 

    The distance from A to C is  of the distance C to B.
    2. A.

    I alone sufficient while II alone not sufficient to answer
    B.

    II alone sufficient while I alone not sufficient to answer
    C.

    Either I or II alone sufficient to answer
    D.

    Both I and II are not sufficient to answer
    E.

    Both I and II are necessary to answer

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    Answer : Option C

    Explanation : 

    .__________.______________________________________.
A     x    C            (100 - x)                 B       

    Let AC = x km. Then, CB = (100 -x) km.
     I. AB = 125% of CB
     100=\( \frac { 125 } { 100 } \)x (100 - x)
     100 - x =\( \frac { 100*100 } {1 2 5} =80\)
     x = 20 km.
     AC = 20 km.
    Thus, I alone gives the answer.
    II. AC =\(\frac { 1 } {4 } \)CB
     x =\(\frac { 1 } {4 } \)(100 - x)
     5x = 100
    x = 20.
     AC = 20 km.
    Thus, II alone gives the answer.

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