(\text{A man wants to cover 100 km. But after cover half distance he become tried and cover the remaining distance } \frac{4}{5} \text{th of his actual speed. For that he able to reach in the destination 1hr late. So how much time man will take to cover the distance?})

Let actual speed be v km/h and actual time be t hours. Distance = 100 km = v*t. First half (50 km) at speed v takes 50/v hours. Second half at (4/5)v takes 50/(4v/5) = 62.5/v hours. Total time = 50/v + 62.5/v = 112.5/v = t + 1. Since v*t = 100, we have 112.5/v = 100/v + 1, giving 12.5/v = 1, so v = 12.5 km/h. Actual time t = 100/12.5 = 8 hours. Total time with fatigue = 8 + 1 = 9 hours.