If a train runs at 40 km/hr, it reaches its destination late by 11 minutes but if it runs at 50 km/hr, it is late by 5 min only. The correct time for the train to complete its journey is:

Question: If a train runs at 40 km/hr, it reaches its destination late by 11 minutes but if it runs at 50 km/hr, it is late by 5 min only. The correct time for the train to complete its journey is:

Solution:
Let the correct time to complete the journey be x min

ATQ,
Distance covered in (x + 11) min at 40 km/hr = Distance covered in (x + 5) min at 50 km/hr
⇒ {(x + 11) × 40}/60 = {(x + 5) × 50}/60
⇒ 2(x + 11)/3 = 5(x + 5)/6
⇒ (2x + 22)/3 = (5x + 25)/6
⇒ 15x + 75 = 12x + 132
⇒ 15x - 12x = 132 - 75
⇒ 3x = 57
⇒ x = 57/3
∴ x = 19

The correct time for the train to complete its journey is 19 min.