Question

Three friends Pradeep, Suresh and Subodh working the same office. During an extended weekend, they decided to go together on a family trip to Corbett National Park. They started from the office in their own car but at a different time and travelled in the same direction at speeds of 50 km/hr, 60 km/hr and 75 km/hr respectively. Suresh and Subodh overtook Pradeep at the same point. If Suresh started 90 minutes after Pradeep, how many minutes after Pradeep did Subodh start from the office?
1. 120
2. 150
3. 180
4. 210
5.

Answer 1

Correct Answer - Option 3 : 180

Calculation:

Given,

The speed of Pradeep = 50 km/hr

The speed of Suresh = 60 km/hr

The speed of Subodh = 75 km/hr

Now, if Suresh started 90 minutes after Pradeep i.e, in 90 minutes Pradeep will travel at a distance of 75km.

By using the relative velocity concept,

Relative velocity = 75/time

⇒ 10 = 75/time

⇒ Time = 7.5 hours

So Suresh will catch Pradeep after 7.5 hours i.e. at a distance of 450km.

Now calculate how long Subodh will cover a distance of 450 km.

⇒ Time is taken by Subodh = 450/75

⇒ Time is taken by Subodh = 6 hours.

Now calculate the total time taken by Pradeep to cover 450 km.

⇒ Time is taken by Pradeep = 450/50

⇒ Time is taken by Pradeep = 9 hours.

To calculate how many minutes after Pradeep did Subodh start from the office subtract Time is taken by Subodh from time is taken by Pradeep.

⇒ Time is taken by Pradeep - Time is taken by Subodh = 9 - 6 = 3 hours = 180 minutes.

Hence option 3 is correct.

Distance is given by the formula Distance = Speed × Time.

When two bodies move in the same direction then the Relative Speed = Difference of Speeds i.e Body A moving with a speed of X km/hr and Body B moving with a speed of Y km/hr and they are moving in the same direction, then the Relative speed = (X - Y) km/hr.