CMAT Clocks Questions

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 . 

A clock is set right at 11 am. The clock gains 12 minutes in a day. 

Clock gaining 12 mins a day implies it is gaining 0.5 minutes for every 1 hour. 
                                        $$\rightarrow$$ Clock gains $$\dfrac{\ 0.5}{60}$$ hours per every hour. 

After 24 hrs, the time in the clock would be 11:12 am the next day. After this time, lets assume "t" hours it takes to show 5pm : 

                                    $$\rightarrow$$ $$11:12+t+\dfrac{\ 0.5\left(t\right)}{60}=17:00$$

                                                    $$t\left(1+\dfrac{\ 1}{120}\right)=5\ hr\ 48\ \min=5.8\ hr$$

                                    $$\rightarrow$$ $$t=\dfrac{\ 5.8}{1+0.0083}=5.752\ hrs$$

Therefore, the correct time should have been = 11:00 am + 5.752 hours = 16:45 hrs. 
Hence, the answer is 45 mins past 4 pm . 

The clock gains 10 minutes in a day.

Therefore, the clock gains 10 minutes in 24 hours.

So, from 3 PM the next day to 10 AM the previous day, time passed = 29 hours.

We know that in 24 hours, the clock gains 10 minutes.

So, in 1 hour, the clock will gain 10/24 minutes.

And, in 5 hours, the clock will gain  = 50/24 minutes = 2.08 minutes approx.

Hence, total time gained = 10+2.8 = 12.08 minutes

So, the true time when the watch indicates 3 pm = 3 pm - 12.08 = 2 pm 48 minutes (approx)

Between 10 A.M. on Monday to 1:00 PM the following day, the watch gained 4.5 minutes. 

So, in 27 hours, the watch gained 4.5 minutes. 

It means, the watch gained every minute in every $$\dfrac{27}{4.5}=6$$ hours

At 10:00 AM, the watch was 2 minutes slow, so the watch would be showing accurate time in next 2*6 = 12 hours i.e. 10:00 P.M.