Question 23

A clock is set right at 8 am. The clock gains 8 minutes in a day. What will be the true time when the watch indicates 11 am the next day?

Solution

It is given clock is set right at 8 am .
Clock gains 8 mins a day .

$$\rightarrow$$ Addition of 8 mins a day is equivalent to adding 1 min per 3 hours . (as in a day there are total 24 hrs).

Now we are supposed to find the true time when clock shows 11 am on the next day :
In a span of 24 hours , the clock gains 8 mins.. So, after 24 hrs i.e next day the time on clock would be 8:08 am ..

After this particular time of 8:08 am , lets say after exactly "t" hours the clock shows 11 am .. But we already know that every hour there is $$\ \dfrac{\ 1}{3}$$min increment which is nothing but $$\dfrac{\ 1}{180}\ hr\ $$ per every hour. Hence :

8:08 am + t + $$\ \dfrac{\ t}{180}$$ = 11:00 am

t(1+ 0.00555) = 2 hrs 52 mins = 2.866 hrs.

Therefore, $$t=\dfrac{\ 2.866}{1.0055}=2.850$$ hours.

Therefore, the original time will be = 8:00 am + 2.850 hrs = 10 : 51 am .

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