After travelling 555 km train met with an accident and speed reduced by 15% of its actual speed and it reaches 6 hours late, if accident had occured after travelling 111 km more, train will reach 5 hours late, find the total distance.

Let original speed = v km/h. After 555 km, speed becomes 0.85v. If accident was 111 km later (at 666 km), delay would be 1 hour less (difference between 6 hours and 5 hours late). The extra 111 km at original speed vs reduced speed accounts for this 1-hour difference. Time difference = 111/v - 111/0.85v = 111/v × (1 - 1/0.85) = 111/v × 0.15/0.85 = 1 hour. Solving gives v = 19.58 km/h. Total distance = 555 + 666 = 1221 km.