Question -
Answer -
Let the original speed of the train be x km/h
and the time taken to complete the journey be y hours.┬а ┬а ┬а ┬а ┬а ┬а тАШ
Then the distance covered = xy km
Case I: When speed = (x + 10) km/h and time taken = (y тАУ 2) h
Distance = (x + 10) (y тАУ 2) km
тЗТ┬а ┬аxy = (x + 10) (y тАУ 2)
тЗТ 10y тАУ 2x = 20
тЗТ┬а 5y тАУ x = 10
тЗТ -x + 5y = 10┬а ┬атАж(i)
Case II: When speed = (x тАУ 10) km/h and time taken = (y + 3) h
Distance = (x тАУ 10) (y + 3) km
тЗТ┬а xy = (x тАУ 10) (y + 3)
тЗТ 3x- 10y = 30┬а ┬а тАж(ii)
Multiplying equation (i) by 3 and adding the result to equation (ii), we get
15y тАУ 10y = 30 f 30
тЗТ 5y = 60
тЗТ┬а ┬аy┬а ┬а= 12
Putting y = 12 in equation (ii), we get
3x- 10 x 12= 30
тЗТ┬а 3x┬а ┬а= 150
тЗТ x┬а ┬а= 50
тИ┤┬а x = 50 and y =┬а ┬а12
Thus, original speed of train is 50 km/h and time taken by it is 12 h.
Distance covered by train = Speed x Time
=┬а 50 x 12 = 600 km.