Question

A man rides his scooter at a speed of 15 km/hr for 20 minutes. Then he reduces his speed to 10 km/hr and drives his scooter for 30 minutes. Now in the last phase, he increases his speed and reaches the destination in the next 10 minutes. Find his speed in the last phase if his average speed was 20 km/hr in the whole journey. 
1. 50 km/hr
2. 60 km/hr
3. 40 km/hr
4. 30 km/hr

Answer 1

Correct Answer - Option 2 : 60 km/hr

Given:

Average speed = 20 km/hr

Rides for 20 minutes at a speed of 15 km/hr

Rides for 30 minutes at a speed of 10 km/hr

Concept Used:

Speed = Distance/Time

Average speed = Total distance travelled/Total time taken

Calculation:

According to the first condition,

⇒ 15 km/hr = Distance/ 20 minutes

⇒ 15 = Distance/ (20/60) hours

⇒ 15 = Distance/(1/3)

⇒ Distance = 5 km

According to the second condition,

⇒ 10 km/hr = Distance/30 minutes

⇒ 10 = Distance/(30/60) hours

⇒ 10 = Distance/(1/2) hours

⇒ Distance = 5 km

Now in the last phase he drives his scooter for 10 minutes.

⇒ Total time = 20 minutes + 30 minutes + 10 minutes

⇒ Total time = 60 minutes

⇒ Total time = 1 hour

Let the distance covered by him in the last phase be x

⇒ Total distance covered = 5 + 5 + x

⇒ Total distance covered = 10 + x

Average speed = Total Distance covered/Total time taken 

⇒ 20 = (10 + x)/ 1 hour

⇒ 20 = 10 + x

⇒ x = 20 – 10

⇒ x = 10 

⇒ The distance covered by him in the last phase is 10 km.

⇒ Speed in the last phase = 10 km/10 minutes

⇒ Speed in the last phase = 10 km/(10/60)hours

⇒ Speed in the last phase = 10 × 6

⇒ Speed in the last phase = 60 km/hr

∴ His speed in the last phase is 60 km/hr.