Question

A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the right time when the clock indicates 10 p.m. on the 4th day?
$
  \left( a \right)\;{\text{8 p}}{\text{.m}} \\
  \left( b \right){\text{ 9 p}}{\text{.m}} \\
  \left( c \right){\text{ 10 p}}{\text{.m}} \\
  \left( d \right){\text{ 11 p}}{\text{.m}} \\
$

Answer 1

Hint – In this problem it is given that the clock losses 16 minutes in every 24 hours, so we simply need to calculate the total number of hours from 5 a.m. till 10 p.m. on the 4th day, then using unitary method we can find the total minutes that will be lost by the clock in those number of hours. Use this concept to get the right answer.

Complete step by step answer:
As we know that in a day there are 24 hours.
It is given that the clock is set at 5 a.m.
So the total time in four days (i.e. 3 complete days and in fourth day from 5 a.m. to 10 p.m. there is 17 hours.)
$ \Rightarrow {\text{Total hours = }}24 \times 3 + 17 = 89$ hours.
Now it is given that in 24 hours the clock loses 16 min.
Therefore 24 hours – 16 mins is 23hrs.44min of this clock are the same as 24 hrs. of the correct clock.
Now as we know $60{\text{ min}} = 1{\text{ hr}}$
Therefore 44 mins = $\dfrac{{44}}{{60}} = \dfrac{{11}}{{15}}$ hrs.
Therefore 23 hrs. 44 min is $\left( {23 + \dfrac{{11}}{{15}}} \right) = \dfrac{{356}}{{15}}$ hrs.
Therefore $\dfrac{{356}}{{15}}$ hrs. of this clock = 24 hrs. of correct clock.
Therefore 1 hrs. of this clock = $\dfrac{{24 \times 15}}{{356}}$ hrs. of correct clock.
Therefore 89 hrs. of this clock = $\dfrac{{24 \times 15}}{{356}} \times 89$ hrs. of correct clock.
Now on simplifying
Therefore 89 hrs. of this clock = 90 hrs. of correct clock.
So the correct time is $\left( {10 + 1} \right)$ p.m. = 11 p.m.
Hence option (d) is correct.

Note – Whenever we face such types of problems the key point is simply to use the unitary method to calculate the time elapsed during the time duration being told. One simple concept that we also need to keep in mind is that 60 minutes comprises 1 hours. This basic understanding will help you get on the right track to reach the answer.