Question

A journey of 200 km has been completed by train A in 3 hours less time than by train B. Find the average of speeds of train A and train B if train B is 15 km/h faster than train A.
1. 25 km/h
2. 32.5 km/h 
3. 35 km/h 
4. 45 km/h 

Answer 1

Correct Answer - Option 2 : 32.5 km/h 

Given :

Let the speed of train A be 'S' km/h 

Let the time to complete the journey by train A be 't'

Let the speed of train B be 'S + 15' km/h 

According to the question 

200/S = t     ....(1) 

200/(S + 15) = t - 3      ....(2)

Subtracting 2 equation from 1 

(200/S) - (200/(S + 15) = 3

S² + 15S = 1000

S² + 15S - 1000 = 0 

⇒ S² + 40S - 25S - 1000 = 0 

⇒ S.(S + 40) - 25.(S + 40) 

⇒ S = 25 km/h 

Speed of A = S = 25 km/h 

Speed oB = S + 15 = 40 km/h 

Average of speeds of A and B = (25 + 40)/2

⇒ 65/2 = 32.5 km/h 

∴ The average of speeds will be 32.5 km/h