A thief steals a bike at 12:30p.m. and drives it at 48km/h. But the theft is discovered after half an hour. The bike owner starts to chase him on another bike at 58km/h. The thief will be caught at ______.

3:24p.m.

Relative speed ( when both moves in same direction ) = 58 - 48 = 10 km/h

As thief steals bike at 12:30 pm . and discovered at 1:00 pm

So , Distance traveled by thief in half hour = \(\frac{48}{2}\) = 24 km

Time taken to caught the thief = \(\frac{24}{10}\)  = 2.4 hour = 2 hour 24 minute

So , thief will be caught at = 1:00 pm + 2 hour 24 minute  = 3:24 pm