A man travels 160 km. in 10 hours . He travels some distance by cycle with the speed of 8 km. / hours and the remaining distance by bike with the speed of 48 km. / hours . Find the distance (in km.) traveled by cycle and bike separately?

Let cycle distance = c, bike distance = b. Total: c + b = 160. Time equation: c/8 + b/48 = 10. Multiply time equation by 48: 6c + b = 480. Subtracting distance equation: 5c = 320, so c = 64. Then b = 160 - 64 = 96. Cycle: 64 km at 8 km/h takes 8 hours. Bike: 96 km at 48 km/h takes 2 hours. Total time = 10 hours. Option C is correct.