Question

A clock gains \[10\] minutes in \[2\] hours. It is set right at \[10:10\] a.m. When the clock shows \[4:40\] p.m. on the same day, what is the correct time?
(A) 4.54 p.m.
(B) 5.00 p.m.
(C) 5.10 p.m.
(D) 4.10 p.m.
(E) None of these

Answer 1

Hint: We are given that a clock gains \[10\] minutes in \[2\] hours. It was set at \[10:10\] a.m. We are asked if the clock shows \[4:40\] p.m. on the same day, what would be the correct time. We will first calculate the time between the starting time, that is, \[10:10\] a.m. and the end time, \[4:40\] p.m. We are given that the clock gains \[10\] minutes in every \[2\] hours, so based on the hours spent, we will add up the extra time being added. And then we will subtract it from the final value to get the correct time. Hence, we will have the correct time of the clock.

Complete step by step answer:
According to the given question, we are given that a clock gains \[10\] minutes in \[2\] hours. It was set at \[10:10\] a.m. We are asked that if the clock shows \[4:40\] p.m. on the same day, what should be the correct time.
Starting time that we are given is \[10:10\]a.m.
And the end time that we are given is \[4:40\] p.m.
We will first calculate the time lapse between the two times and which we can see clearly to be 6 hours.
So after every 2 hours, \[10\] minutes is added to the actual time, that is,
At \[12:10\]p.m. , \[10\] minutes is added to the actual time and so the clock will display \[12:20\] p.m.
And again at \[2:10\]p.m. , \[10\] minutes is added to the actual time and so the clock will display \[2:30\] p.m.
And once more at \[4:10\]p.m. , \[10\] minutes is added to the actual time and so the clock will display \[4:40\] p.m.
So, until the end time, 30 minutes had been added to the clock.

So, the correct answer is “Option C”.

Note: The solution should be done step wise, as the steps get trickier as you continue to solve it. The extra time added to the clock should be reflected in calculations or else the calculations will give incorrect answers. Also, after each 2 hours, the extra time should be added to the previously added time and not to the actual time.