Question

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

Quantity I: Two trains when traveling in the same direction takes 55 seconds to cross each other whereas train 1 will take 20 seconds to cross a station master on a platform. The length of trains 1 and 2 are the same which is 220m. (train 1 is faster than train 2)

Quantity II: A car moves parallel to a train track and on seeing the train move beside it, the car decides to race the train. If the car crosses the train in 20 seconds, find the speed of the train, the given car has to travel 200 m to cross the train at 18 m/s.

1. Quantity I < Quantity II
2. Quantity I ≤ Quantity II
3.

Quantity I > Quantity II

4. Quantity I ≥ Quantity II
5. Quantity I = Quantity II or relation cannot be established

Answer 1

Correct Answer - Option 1 : Quantity I < Quantity II

Given: 

Quantity I:

Time by which train 1 and train 2 will cross each other traveling in the same direction = 55 s

Time by which train 1 will cross the station master = 20 s

Length of train 1 and 2 = 220 m  

Quantity II:

Time in which car crosses the train = 20 s

Length of train = 200 m

Speed of the car = 18 m/s

Concept used:

Speed, S = Distance/Time

The relative speed of two objects moving in the same direction = S₁ – S₂

Where ‘S’ is speed.

Calculation:

Quantity I:

Time taken to cross each other = 55 s = (2 × 220)/(S_T1 – S_T2)

⇒ S_T1 – S_T2 = 8 m/s

Time taken by train 1 to cross station master = 20 s = 220/S_T1

⇒ S_T1 = 11 m/s

Then, speed of train 2 = 11 – 8 = 3 m/s

Quantity I = 3 m/s

Quantity II:

Time taken by car to cross the train = 20 s = 200/(S_T - 18)

⇒ Speed of the train, S_T = 18 + 10 = 28 m/s

Quantity II = 28 m/s

Quantity I	Relation	Quantity II
3 m/s	<	28 m/s

 

∴ From the table it is clear that, Quantity I < Quantity II.