Time and Distance - Aptitude Questions and Answers - RejinpaulPlacement

DATA SUFFICIENCY TYPE QUESTIONS
Directions (Question 64 to 70) :
Each of the questions 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 statements is/are sufficient to answer the question. Read both the 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 answerer 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; and
Give answer (e) if the data in both Statements I and II together are necessary to answer the question.

64.
How much time did X take to reach to destination? [M.B.A 2002]
I. The ratio between the speeds of X and Y is 3 : 4.
II. Y takes 36 minutes to reach the same destination.

Answer: (e) if the data in both Statements I and II together are necessary to answer the question.

Solution:   I. If Y takes 4 min, then X takes 3 min.
II. If Y takes 36 min, then X takes [(3/4) * 36] min = 27 min.

Thus, I and II together give the answer

65.
What is the usual speed of the train?
I. The speed of the train is increased by 25 km/hr to reach the destination 150 km away in time.
II. The train is late by 30 minutes.
Answer: (e) if the data in both Statements I and II together are necessary to answer the question.

Solution:   Let the usual speed of the train be x kmph.
Time taken to cover 150 km at usual speed = 150/x hrs.

I. Time taken at increased speed = 150 / (x + 25) hrs.
II. 150/x - 150/(x + 25) =30/600
=> 1/x - 1/(x + 25) = 1/300
=> [(x + 25) - x] * 300 = x (x + 25)
=> x2 + 25x - 7500 = 0
=> (x + 100) (x - 75) = 0
=> x = 75

Thus I and I together give the answer
66.
Two towns are connected by railway. Can you find the distance between them? [M.B.A 2001]
I. The speed of 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.

Answer: (d) if the data even in both Statements I and II together are not sufficient to answer the question
Solution:   Let the distance between the two statements be x km.

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

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

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

67.
The two 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 A from C? [M.B.A 2003]
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 1/4 of the distance from C to B.
Answer: (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question

Solution:   Let AC = x km. Then CB = (100 - x) km.

I. AB = 125% of CB
=> 100 = 125/100 * (100 - x)
=> 100 - x = (100 * 100)/125 = 80
=> x = 20 km.
AC = 20 km.
Thus, I alone gives the answer.

II. AC = 1/4 CB
=> x = 1/4 (100 - x)
=> 5x = 100
=> x = 20.
AC = 20 km.
Thus, II alone gives the answer.

68.
What is the average speed of the car over the entire distance?
I. The car covers the whole distance in four equal stretches at speeds of 10 kmph, 20 kmph, 30 kmph and 60 kmph respectively
II. The total time taken is 36 minutes.
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

Solution:   Let the whole distance be 4x km.

I. Total time taken = (x/10 + x/20 + x/30 + x/60)
= (6x + 3x + 2x + x) / 60
= 12x/60 = x/5

Speed = Distance/Time = 4x / (x/5) kmph = 20 km/hr.

I alone is sufficient to answer the question.

II alone does not give the answer.

69.
A car and a bus start from city A at the same time. How far is the city B from city A?
I. The car travelling at an average speed of 40 km/hr reaches city B at 4:35 p.m.
II. The bus reaches city B at 6:15 p.m. at an average speed of 60 km/hr.
Answer: (e) if the data in both Statements I and II together are necessary to answer the question.

Solution:   Let AB = x km.
From I and II, we get:
x/40 - x/60 = 1 40/60 [(6:15 p.m.) - (4:35 p.m.) = 1 hr 40 min]
=> x/40 - x/60 = 100/60. This gives x.

70.
Two cars pass each other in opposite direction. How long would they take to be 500 km apart? [M.A.T 1998]
I. The sum of their speeds is 135 km/hr.
II. The difference of their speeds is 25 km/hr.