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Time and Distance - General Aptitude

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
  • Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
  • Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
Q1:

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

ANS:C - Either I or II alone sufficient to answer 

.__________.______________________________________. A x C (100 - x) B
Let AC = x km. Then, CB = (100 -x) km.  I. AB = 125% of CB
 100 = 125 x (100 - x)
100
 100 - x = 100 x 100 = 80
125
 x = 20 km.  AC = 20 km. Thus, I alone gives the answer.
II. AC = 1 CB
4
 x = 1 (100 - x)
4
 5x = 100 x = 20.  AC = 20 km. Thus, II alone gives the answer.  Correct answer is (C).