Aptitude - Problems on Trains

Each of these questions is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.

1. 

At what time will the train reach city X from city Y?

I. 

The train crosses another train of equal length of 200 metres and running in opposite directions in 15 seconds.

II. 

The train leaves city Y at 7.15 a.m. for city X situated at a distance of 558 km.

 III. 

The 200 metres long train crosses a signal pole in 10 seconds.

A. I only
B. II only
C. III only
D. II and III only
E. All I, II and III are required.

Answer: Option D

Explanation:

From the statement I, we get length of the train is 200 metres (Redundant info while comparing with Statement III). The rest of the info given in this statement cannot be used for calculating the speed of the train, because the two trains might run at different speed.

III gives, speed = 200 m/sec = 20 m/sec = 20 x 18 km/hr = 72 km/hr.
10 5

II gives, time taken = 558 hrs = 31 hrs = 7 3 hrs = 7 hrs 45 min.
72 4 4

So, the train will reach city X at 3 p.m.

Hence II and III only gives the answer.


2. 

What is the length of a running train P crossing another running train Q?

I. 

These two trains take 18 seconds to cross each other.

II. 

These trains are running in opposite directions.

 III. 

The length of the train Q is 180 metres.

A. I only
B. II only
C. III only
D. All I, II and III are required
E. Even with I, II and III, the answer cannot be obtained.

Answer: Option E

Explanation:

Let the length of the train P be x metres.

 II. These trains are running in opposite directions.

III. Length of the train Q is 180 m.

  I. Time taken by P to cross Q = (180 + x)     18 = (180 + x)
Relative speed Relative speed

Thus, even with I, II and III, the answer cannot be obtained.

Correct answer is (E).