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(B) The total time interval from Monday $12$ noon to the following Monday $2$ p.m. is $7$ days and $2$ hours,which equals $170$ hours.The total gain i

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$2$ p.m. on Wednesday

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(B) The total time interval from Monday $12$ noon to the following Monday $2$ p.m. is $7$ days and $2$ hours,which equals $170$ hours.The total gain in time is $2$ minutes (to reach zero error) $+ 4$ minutes $48$ seconds (to reach the fast state).$4$ minutes $48$ seconds $= 4 + \frac{48}{60} = 4 + \frac{4}{5} = \frac{24}{5}$ minutes.Total gain $= 2 + \frac{24}{5} = \frac{34}{5}$ minutes in $170$ hours.To be correct,the watch must gain $2$ minutes.Time taken to gain $2$ minutes $= \frac{170}{(34/5)} 	imes 2 = \frac{170 	imes 5 	imes 2}{34} = 5 	imes 5 	imes 2 = 50$ hours.$50$ hours $= 2$ days and $2$ hours.Starting from Monday $12$ noon,$2$ days and $2$ hours later is Wednesday $2$ p.m.

$A$ watch which gains uniformly is $2$ minutes slow at noon on Monday and is $4$ minutes $48$ seconds fast at $2$ p.m. on the following Monday. When was it correct?

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