In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs., 18 ...
In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs., 18 min., 15 seconds of watch time. What is the time gained or lost by this watch in one day?
Answer/Solution
13 min. 50 seconds lost
Steps/Work
In a watch than is running correct the minute hand should cross the hour hand once in every 65 + 5⁄11 min.
So they should ideally cross 3 times once in
3×(720/11)−2060/11min=196.36minutes
But in the watch under consideration, they meet after every 3 hr,18 min and 15 seconds,
i.e, (3 × 60 + 18 + 15⁄60) = 793⁄4 min.
Thus, our watch is actually losing time (as it is slower than the normal watch). Hence when our watch elapsed
(1440×196.36/198.25)=1426.27.
Hence the amount of time lost by our watch in one day = (1440 - 1426.27) = 13.73 i.e. 13 min and 50s (approx).
Answer B
So they should ideally cross 3 times once in
3×(720/11)−2060/11min=196.36minutes
But in the watch under consideration, they meet after every 3 hr,18 min and 15 seconds,
i.e, (3 × 60 + 18 + 15⁄60) = 793⁄4 min.
Thus, our watch is actually losing time (as it is slower than the normal watch). Hence when our watch elapsed
(1440×196.36/198.25)=1426.27.
Hence the amount of time lost by our watch in one day = (1440 - 1426.27) = 13.73 i.e. 13 min and 50s (approx).
Answer B