# Aptitude - Time and Distance

Exercise : Time and Distance - Data Sufficiency 1
Directions to Solve

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.

1.
 Two towns are connected by railway. Can you find the distance between them? I. The speed of the mail train is 12 km/hr more than that of an express train. II. A mail train takes 40 minutes less than an express train to cover the distance.
I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Explanation:

Let the distance between the two stations be x km.

I. Then, speed of the mail train = (y + 12) km/hr.

 II. x - x = 40 . y (y + 12) 60

Thus, even I and II together do not give x.

2.
 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.
I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Explanation:

```.__________.______________________________________.
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.

3.
 Two cars pass each other in opposite direction. How long would they take to be 500 km apart? I. The sum of their speeds is 135 km/hr. II. The difference of their speed is 25 km/hr.
I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Explanation:

I gives, relative speed = 135 km/hr.

 Time taken = 500 hrs. 135

II does not give the relative speed.

I alone gives the answer and II is irrelevant.

4.
 How much time did X take to reach the destination? I. The ratio between the speed of X and Y is 3 : 4. II. Y takes 36 minutes to reach the same destination.
I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Explanation:

Since ratio of speed of X : Y is 3 : 4, then ratio of time will be 4 : 3.

I. If Y takes 3 min, then X takes 4 min.

 II. If Y takes 36 min, then X takes 4 x 36 min = 48 min. 3

Thus, I and II together give the answer.