Question

Abdul travelled 300 km by train and 200 km by bus in 5 h 30 min. If he had travelled 260 km by train and 240 km by bus he would have taken 6 min. Longer find speed of train and bus

Answer 1

1st case :
              distance travelled by train = 300km
                        and by taxi = 200km
    
          Let speed of train be x km/hr     and     that of taxi be y km/hr.
                   
      so, time taken by train = d/s                        time taken by taxi = d/s
                                       = 300/x                                                = 200/y
   
                total time taken = 5hrs 30 mins = 5 1/2 hrs
                                  
           so, 300/x +200/y = 5 1/2 by solving we get : 600y + 400x = 11xy..........1

2nd case :
           
            distance travelled by train = 260 km          and by taxi = 240 km
           
     here also speed of train be x km/hr and of taxi be y km/hr
 
 Then time = d/s
          train time= 260/x hr                            of taxi = 240/y hr
        combiningly,total  time =
 
                             260/x + 240/y = 5hrs 36 mins
                       =>  or 260/x + 240/y = 5 3/5   on solving we get,
   
                      1300y + 1200x = 28xy...............2

eq 1 × 3 = 1800y + 1200x = 33xy
 
 on solving 1 and 2 we get:
         x=100 km/hr
        y= 80 km/hr

Hope This helps :)