Question

My watch was 8 minutes behind at 8 pm on Sunday but within a week at 8 pm on Wednesday it was 7 minutes ahead of time. During this period at which time this watch has shown the correct time :

• A. Tuesday 10 : 24 am
• B. Wednesday 9: 16 pm
• C. It cannot show the correct time during this period
• D. None of the above

Answer 1

Answer: (A)

Tuesday 10 : 24 am

The answer is option $$

Let's assume there a clock $A$ which runs accurately.

Let's call our watch as $B$

Speed of clock $A=60min/hr$

From Sunday $8pm$ till Wednesday $8pm,$ $A$ covers $(3\times 24\times 60)mins=4320mins$

In the same time minutes covered by $B=4320+8+7=4335mins$

$\therefore$ Speed of $B=4335/\left(3X24\right)=60\frac{5}{24}mins/hr$

Relative velocity of $B$ wrt $A=60\frac{5}{24}-60=\left(5/24\right)min/hr$

To show the correct time, the watch $B$ needs to cover up $8mins$ wrt $A$

Time taken by $B$ to cover $8mins$ wrt $A=\frac{8}{\left(\frac{5}{24}\right)}=8\times \frac{24}{5}=38.4hrs=38hrs24mins$

On Tuesday at $10am$ it would have been $38$ hours from Sunday $8pm$

So on Tuesday $10:24am$ the watch will show correct time