Question

A clock is set right at 5 : 00 a.m. The clock loses 16 minutes in 24 hours. What will be the right time when the clock indicates 10 : 00 p.m. on the fourth day ?

Answer 1

Hint: The clock here sets is 16 minutes back to the normal clocks. The most important thing that we should keep in mind is that this is not the 24 hours of all the four days. On the fourth day the time is measured only till 10 : 00 p.m.

Complete step-by-step answer:
Let us firstly calculate the time duration in hours from 5 : 00 a.m. of the first day to the 10 : 00 p.m. of the fourth day.
As we all know that
\[1{\text{ }}day = 24{\text{ }}hours\]
and if started calculating time from 5 : 00 a.m. on the first day then the 24 hours of all the four days will complete on 5 : 00 a.m. of the fourth day.
But the time here is measured till 10 : 00 p.m.
So the hours that are less to complete the 24 hours of fourth day must be the hours less than 5 : 00 a.m. to 10 : 00 p.m. ( i.e. 7 hours )
So the hours that we will count on fourth day is
\[\left( {{\text{24}} - {\text{7}} = {\text{17}}} \right)\]
So the total time in hours is equal to the 24 hours of three days and 17 hours of fourth day i.e. \[\left( {{\text{3}} \times \left( {{\text{24}}} \right) + {\text{17}}} \right) = \left( {{\text{72}} + 17} \right) = {\text{89hours}}\]
Now as we know this clock is 16 minutes back than normal clock which means that
23 hours 44 minutes in this clock must be equal to the 24 hours of the normal
\[\left( {23{\text{hours }}44{\text{minutes }} = 24{\text{hours}}} \right)\]
As we know that ( 1 hour = 60 min )
So to convert 44 minutes into hours we had to divide it by 60
So \[\left( {\dfrac{{1424}}{{60}}{\text{hours }} = 24{\text{hours on normal clock}}} \right)\]
Now taking L.C.M of L.H.S we will solve this
\[ = \left( {\dfrac{{1424}}{{60}}{\text{hours }} = 24{\text{hours on normal clock}}} \right) = \]\[\left( {\dfrac{{{\text{356}}}}{{{\text{15}}}}{\text{ hours = 24hours on normal clock}}} \right)\]
Now on further solving we will get that
\[\]
And here the total time is 89 hours so we have to find that 89 hours on this clock is equal to how many hours on normal clock
So \[{\text{89 hours on this clock}} = 89 \times \left( {24 \times \dfrac{{15}}{{356}}{\text{hours of normal clock}}} \right)\]
On further solving it we get that
\[{\text{89 hours}} = \left( {\dfrac{{32040}}{{356}}} \right){\text{hours of this clock}} = \left( {9{\text{0}}} \right){\text{ hours}}\]
So at the completion of 89 hours on this clock ( i.e. 10 : 00 p.m. ) is equal to the 90 hours of the normal clock that means at completion of 89 hours on this clock the correct clock is exactly 1 hour before
Hence the timing on the correct clock is 11 : 00 p.m. when the time on this clock is 10 : 00 p.m.

NOTE :- In such a question it is mandatory to change the days into the hours. And while calculating the hours we should keep in mind that the days which are fulfilling the conditions of a completion ( i.e. 24 hour = 1 day ) for such days we need not to count the hours. We can simply do the product in a number of days within 24 hours.