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Aptitude Day 279

Problems on Time and Distance: 

1. A walks around a circular field at the rate of 1 round per hour while B runs around it at the rate of 3 rounds per hour. They start in the same direction from the same point at 8.30 A.M. they shall 1st cross each other at:

Solution:
                 Since they move in the same direction along the circle, they’ll 1st meet each other when there is a difference of 1 round between the 2.

                  Relative speed = 3-1 
                                          = 2 rounds/ hour.

                  Time taken to complete 1 round at his speed = 1/2 hr 
                                                                                         = 30 minutes.

2. A thief steals a car at 4.30 PM and drives it at 80 km/hr. The theft is discovered at  5 PM and the owner sets off in another car at 90 km/hr. When will he overtake the thief?

Solution:
                  Consider, the thief is overtaken x hours after 4.30 PM.

                  Distance covered by thief in x hours = distance covered by the owner in (x-1/2) hours.

                  80x = 90(x-1/2)

                  By solving this, we get
                  x = 9/2
                     = 4.5 hours.

                  The thief is overtaken at 9 PM.


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