Previous Year Questions

Let speed of train A = s km/h

From statement I: Train A of length 4y meters can cross two platforms of lengths 2y meters and 4y - 20 meters in 6 seconds and 7 seconds respectively.

6 = (4y + 2y)/s

s = y

And, 7 = (4y + 4y - 20)/s

7s = 8y - 20

Now, 7s = 8s - 20

s = 20

So, statement I alone is sufficient.

From statement II: Train B of length 5y meters can cross a pole in 6.25 seconds.

So, 6.25 = 5y/(speed of train B)

Speed of train B = 0.8y

From statement III: While moving in same direction, train A can cross train B in 45 seconds.

Train A crossing train B. so, speed of train A is greater than speed of train B.

Now, relative speed = speed of train A - speed of train B = s - speed of train B

And 45 = (length of train A + length of train B)/(s - speed of train B)

From statement IV: With 20% less speed, train A can cross a pole in 5 seconds.

5 = length of train A/(80% of s)

s = Length of train A/4

Sum of lengths of train A and train B is 9y meters.

Length of train A + length of train B = 9y

From statements II and III together:

45 = (length of train A + 5y)/(s - 0.8y)

One equation and three variables are there, so, these two statements together are not sufficient to find the speed of train A.

From statements II and IV together:

Length of train A = 9y - 5y = 4y

s = 4y/4

s = y

Value of y is unknown. So, these two statements together are not sufficient to find the speed of train A.

From statements III and IV together:

45 = 9y/(s - speed of train B)

s = Length of train A/4

Two equations and 3 variables are there, so, these two statements together are not sufficient to find the speed of train A.

From statements II, III and IV together are not sufficient to find the speed of the train A.

Hence, only statement I alone is sufficient to find the answer.