Question

A distance of 150 km is covered by the Satabdi train in 5 hours less than by Rajdhani train. Find the time taken by Rajdhani train to cover the whole journey, if the Rajdhani train is 5 km/h slower than the Satabdi train.  
1. 10 hours 
2. 15 hours 
3. 20 hours 
4. 25 hours 

Answer 1

Correct Answer - Option 2 : 15 hours 

Given :

A distance of 150 km is covered by the Satabdi train in 5 hours less time than by Rajdhani train.

Rajdhani train 5 km/h slower than the Satabdi train.  

Formula used :

Time = Distance/Speed 

Calculations :

Let the speed of the Rajdhani train be 'S' km/h 

Let the time taken by Rajdhani train be 't' hours

Let the speed of the Satabdi train be 'S + 5' km/h 

Let the time taken by Satabdi train be 't - 5' hours 

Time taken by Rajdhani train = 150/S       

150/S = t      ....(1)

Time taken by Satabdi train = 150/(S + 5)     

150/(S + 5) = t - 5      ....(2)  

Subtract equation 2 from 1 

150/S - 150/(S + 5) = 5 

Solving it further we get a quadratic equation 

S² + 5s = 150 

⇒ S² + 5S - 150 = 0 

⇒ S² + 15S - 10S - 150 = 0 

⇒ S.(S + 15) - 10.(S + 15) = 0 

⇒ S = 10 and - 15 

So, 

S = 10 km/h Now, 

Time taken by Rajdhani train to cover the distance = 150/10 

⇒ 15 hours 

∴ The time taken by Rajdhani train to complete the journey will be 15 hours