Question

A train running at the speed of 72 km/hr crosses a platform which is 50% longer than the length of the train in 20 seconds. If a train crosses a car moving in same direction in 36 seconds. The speed of the car is x km/hr. Find the value of x. (Neglect the length of the car)
1. 56 km/hr
2. 50 km/hr
3. 40 km/hr
4. 60 km/hr
5. None of these

Answer 1

Correct Answer - Option 1 : 56 km/hr

Given:

Let the speed of the car be x

Speed of the train = 72 km/hr

Concept:

In these types of questions, we find the length of the train from 1^st condition and then find the value of x using the relative speed concept.

Formula:

Distance = speed × time

Relative speed = S₁ – S₂ (when trains move in the same direction)

x km/hr = x × (5/18) m/s

Calculation:

Let the length of the train be ‘l’

⇒ Length of the platform = (150/100) × l = (3/2) l

Distance = length of the train + length of the platform = speed of train × time

⇒ l + (3/2) l = 72 × 5/18 × 20

⇒ 5l/2 = 400

⇒ l = 160 m

Now,

160 = (72 – x) × (5/18) × 36

⇒ 160 = (72 – x) × 10

⇒ 16 = 72 – x

⇒ x = 56 km/hr

∴ The speed of the car = 56 km/hr