Discussion
A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
Answer: B
From 8 am Sunday to 8 pm the following Sunday is
\[ 7 \times 24 + 12 = 180 \text{ hours} \]
\[ \text{total gain} = 5 + 5\tfrac{4}{5} = 10.8 \text{ minutes} \]
\[ \text{rate} = \frac{10.8}{180} = 0.06 \text{ min per hour} \]
Starting 5 minutes slow, it becomes correct after
\[ \frac{5}{0.06} = 83\tfrac{1}{3} \text{ h} = 83 \text{ h } 20 \text{ min} \]
\[ 8 \text{ a.m. Sunday} + 83 \text{ h } 20 \text{ min} = 7{:}20 \text{ p.m. on Wednesday} \]
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