Question

A watch loses $3\%$ time during the first week and then gains $2\%$ time during the next one week. If the watch was set right at $12$ noon on a sunday, what will be the time that the watch will show exactly $14$ days from the time it was set right $?$

Answer 1

Finding the right time:

Number of hours in a week$=7x24=168hours$

The watch loses $3\%$ time during the first week.

Therefore,$3\%of168=5.04hours$

During the next week, the watch gains $2\%$ of the time

$\therefore 2\%of168=3.36hours$

Now the net value of hours with $3\%$ loss and $2\%$gain is$=-5.04+3.36=-1.68hour$

Therefore, if the clock is set at $12$ noon two weeks from the time it was set right is

$$\begin{gathered} =1hourand40.8minutes \\ =12-(1hour+40minutes+48seconds). \end{gathered}$$

Hence, the required time is $10:19:12$.