Discussion :: Time and Distance

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.
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 
Answer : Option C
Explanation :
.__________.______________________________________. A x C (100  x) BLet 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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