The watch which gains uniformly is 2 minutes | vedclass

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Question

(A) From Sunday noon to the following Sunday at $2$ $pm$, the total time elapsed is $7$ days and $2$ hours.Total time $= (7 	imes 24) + 2 = 170$ hour

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$2$ $pm$ on Tuesday

Vedclass · Answer

(A) From Sunday noon to the following Sunday at $2$ $pm$, the total time elapsed is $7$ days and $2$ hours.Total time $= (7 	imes 24) + 2 = 170$ hours.In this period, the watch gains $2$ minutes (to reach correct time) $+ 4$ minutes $48$ seconds (to go fast).Total gain $= 6$ minutes $48$ seconds $= 6 + \frac{48}{60} = 6 + \frac{4}{5} = \frac{34}{5}$ minutes.Since the watch gains $\frac{34}{5}$ minutes in $170$ hours, it gains $1$ minute in $\frac{170 	imes 5}{34} = 25$ hours.To be correct, the watch must gain $2$ minutes from its initial slow state.Time required $= 2 	imes 25 = 50$ hours.$50$ hours $= 2$ days and $2$ hours.Adding $2$ days and $2$ hours to Sunday noon: Sunday noon $+ 2$ days $=$ Tuesday noon. Tuesday noon $+ 2$ hours $= 2$ $pm$ on Tuesday.

The watch which gains uniformly is $2$ minutes slow at noon on Sunday and is $4$ minutes $48$ seconds fast at $2$ $pm$ on the following Sunday. When was the watch correct?

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