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Duration of Time

A Watch Which...

Question

A Watch Which Gains Uniformly is $5 m i n$ , Slow At $8$ O'clock In The Morning On Sunday And It Is $5 M i n 48 S e c .$ 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 $= 7 d a y s 12 h o u r s = 180 h o u r s$
Therefore, the watch gains $\frac{5}{54} m i n$ in $180 h o u r s$
Now, $\frac{5}{54} m i n$ are gained in $180 h o u r s$
Therefore, $5 m i n$ are gained in $(180 \times \frac{5}{54} \times 5) h r s . = 83 h r s 20 m i n .$
$= 3 d a y s 11 h r s 20 m i n .$
Therefore, the watch is correct $3 d a y s 11 h r s 20 m i n .$ after $8 a . m .$ on Sunday
Therefore, it will be correct at $20 m i n p a s t 7 p . m .$ on Wednesday

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