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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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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 = 100x = 20. AC = 20 km.Thus, II alone gives the answer.