A cyclist, after riding a certain distance, stopped for half an hour to repair his bicycle, after which he completes the whole journey of 30km at half speed in 5 hours.  If the breakdown had occurred 10km farther off, he would have done the whole journey in 4 hours. Find where the breakdown occurred and his original speed. (Ans: 10km, 10km/hr)

Ans:    Let x  be the place where breakdown occurred y be the original speed

x/y + (30 - x)/(y/2) = 5

x + 10/y + 30 - ( x + 10)/(y/2) = 4

x/y + 60 - 2 x/y = 5

On solving, we get, x = 10 km and y = 10 km/h