In a watch, the minute hand crosses the hour hand for the third time exactly after 3 hrs., 18 min., 15 seconds of actual time. What is the time gained or lost by this watch in one day?
a) 14 min, 10 seconds lost
b) 13 min, 50 seconds lost
c) 13 min, 20 seconds gained
d) 14 min, 40 seconds gained
Ans: b) 13 min, 50 seconds lost
In a correctly running watch, the crossing of hands should take place exactly after every (720/11) = 65 5/11 minutes. In this watch, it takes place after [(3 hours, 18 minutes, 15 seconds)/3] = (1 hour), 6 minutes, 5 seconds , i.e. 66 5/60 minutes of actual time. Thus the watch takes a longer time to accomplish the task as compared to a correctly running watch. So this watch loses time = [(66 5/60) – (65 5/11)] = (83/132) minutes in 65 5/11 minutes of correct time. So in 1 day i.e. (24 × 60) minutes of correct time, it will lose (83/6) minutes, i.e. 13 minutes 50 seconds.
