Question

# A Watch Which Gains Uniformly is$5min$, Slow At $8$ O'clock In The Morning On Sunday And It Is $5Min48Sec.$ Fast At $8$ p.m. On Following Sunday. When Was It Correct?

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Solution

## Time from $8$ a.m on Sunday to $8$ p.m on the following Sunday $=7days12hours=180hours$Therefore, the watch gains $\frac{5}{54}min$in $180hours$Now, $\frac{5}{54}min$ are gained in $180hours$Therefore, $5min$ are gained in $\left(180×\frac{5}{54}×5\right)hrs.=83hrs20min.$ $=3days11hrs20min.$Therefore, the watch is correct $3days11hrs20min.$ after $8a.m.$ on SundayTherefore, it will be correct at $20minpast7p.m.$ on Wednesday

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