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.

The speed of a 800 meters long Rajdhani express is 10 km per hour more than that of a truck. If the truck and Rajdhani express travel in opposite directions then the truck can cross Rajdhani express completely in 2 minutes. (Neglect the length of truck)

Quantity I: What is the speed of Rajdhani express?

Quantity II: What will be the speed of truck when it is increased by 75%?
1. Quantity 1 > Quantity 2
2. Quantity 1 ≥ Quantity 2
3. Quantity 1 < Quantity 2
4. Quantity 1 ≤ Quantity 2
5. Quantity 1 = Quantity 2

Answer 1

Correct Answer - Option 1 : Quantity 1 > Quantity 2

Given:

Length of train = 800 m

Speed of train = 10 km/hr more than truck

Formula used:

Relative speed (Opposite direction) = a + b

D = S × T

D = Distance

S = Speed

T = Time

Calculations:

Let the speed of truck = x km/hr

⇒ speed of rajdhani express = x + 10 kmph

⇒ If they travel in opposite direction then the relative speed = (x + x + 10) km per hr

⇒ (2x + 10) × (5 / 18)

⇒ 800/120 m/s = (2x + 10) × (5 / 18)  m/s

⇒ 20/3 m/s = (2x + 10) × (5 / 18)  m/s

⇒ 20 m/s = (2x + 10) × (5 / 6)  m/s

⇒ 4 m/s = (2x + 10) × (1 / 6)  m/s

⇒ 2x + 10 = 24

⇒ x = 7 km/hr

Quantity I:

The speed of the train = x + 10 = 17 km per hr

Quantity II :

175% of 7 = 175 × 7 / 100

⇒ 175% of 7 = 12.25 km/hr

∴ Quantity 1 > Quantity II