Question

At a railway station a 24 hour watch loses 3 minutes in 4 hours. If it is set correctly on Sunday noon when will the watch show the correct time?

• A. 6 pm after 40 days
• B. 12 noon after 75 days
• C. 12 pm after 100 days
• D. 12 noon after 80.days

Answer 1

The correct option is D 12 noon after 80.days

The answer is option $D$

The station clock loses $3$ mins in $4$ hours

t$\Rightarrow$ Instead of moving my $240$mins, the clock covers only $237$ mins

So the velocity of the clock $=\frac{(237\times 60)}{240}=59.25min/hr$

Relative velocity of the clock wrt an accurate clock $(60-59.25)=0.75min/hr$

To show the correct time wrt to an accurate clock, the station clock has to make up $24$ hrs wrt to an accurate clock

Time take to make up this $24$ hrs $($ or $24\times 60$ min$)=(24\times \frac{60}{0.75})=24\times 80hrs=80days$