**Directions:** In the following question, two statements are numbered as Statement I and II. On solving these statements we get Quantity I and II respectively. Solve the given statements for both quantities and choose the correct option.

Quantity I: A train of the length 450 m moving with a speed of 45 km/hr. Find the time taken by the train to cross a post on a platform of length 450m.

Quantity II: Two trains, A of length 300 m and B of length 400 m are moving in parallel tracks in the same direction. Find the time taken by the guard of train A to pass the train B given the speed of train A and B is 30 m/s and 20 m/s respectively.

Option 3 : Quantity II > Quantity I

**Given**

Quantity I:

Length of train = 450 m

Speed of train = 45 km/hr

Quantity II:

The length and speed of train A are 300 m and 30 m/s respectively.

The length and speed of train B are 400 m and 20 m/s respectively.

**Concept**

For quantity I:

Time taken to cross the post = length of train/speed of the train

For quantity II:

Time taken by train A to cross guard of train B = length of train B/(relative speed of A to B)

**Relative speed**: We need to use relative speed as both trains A and B are moving.

As both trains, A and B are moving in the same direction,

Relative speed = speed of train A – speed of train B

**Calculation**

Quantity I:

Time taken to cross the post = length of train/speed of the train

Length of train = 450 m

Speed of train = 45 km/hr

⇒ Speed of train = 25/2 m/s

⇒ Time taken to cross the post = 450/(25/2) s

⇒ Time taken to cross the post = 36 s

Quantity II:

Speed of train A = 30 m/s

Speed of train B = 20 m/s

The relative speed of A to B = speed of train A – the speed of train B

⇒ The relative speed of A to B = 30 – 20 m/s

⇒ The relative speed of A to B = 10 m/s

Time taken by train A to cross guard of train B = length of train B/(relative speed of A to B)

⇒ Time taken by train A to cross guard of train B = 400/10

⇒ Time taken by train A to cross guard of train B = 40 s

Comparing the results obtained in quantity I and II

Quantity I |
Relation |
Quantity II |

36 s |
< |
40 s |

From the above table, we can conclude that value of quantity I is less than the value of Quantity II.