Question

A driver is driving a car from Mumbai to Pune at a speed of 50 km/h. The distance between the two cities is 300 km. By what percentage, should the driver increase the speed of the car, so that he can reach 10 minutes before the usual time he takes to complete the journey?
1. 11/7
2. 13/7
3. 23/7
4. 20/7
5. 18/7

Answer 1

Correct Answer - Option 4 : 20/7

Given:

The distance between Mumbai and Pune = 300 km

Usual speed of the car = 50 km/h

Formula Used:

Time = Distance/Speed

Increased Speed = [(100 + percentage increase in speed)/100] × usual speed

Calculation:

The usual time taken to complete the journey from Mumbai to Pune is given by:

300/50 = 6 hours

∵ The time taken to complete the journey should be reduced by 10 minutes,

The required time to complete the journey, with the increased speed is given by

6 - 10/60 = 35/6 hours

The increased speed = distance/reduced time

⇒ Increased speed = 300/(35/6) = 360/7 km/h

The percentage increase in speed is given by 

{[(360/7) - 50]/50} × 100 = [(360 - 350)/7] × 2

⇒ [(360 - 350)/7] × 2 = 20/7 %

∴ The required percentage increase in the speed of the car is 20/7 %