Question

There are two clocks, both sets to show the correct time at 9:00 AM. One clock loses 1 minute every hour and the other gains 1 minute every hour. By how many minutes do they differ at 10:00 PM on the same day? Choose the correct option.
(A). 24 minutes
(B). 30 minutes
(C). 28 minutes
(D). 26 minutes
(E). 13 minutes

Answer 1

Hint: First, calculate the difference in time between both the clocks in 1 hour and then use the unitary method to calculate the difference between 9:00 AM to 10:00 PM, i.e. 13 hours.

Complete step-by-step solution -
In the question, we have to find the time difference between two clocks between 9:00 AM to 10:00 PM, i.e. in 13 hours.
Now, one clock loses 1 minute every hour, so the first clock shows 59 minutes every hour.
Also, the second clock gains 1 minute every hour, so the second clock shows 61 minutes every hour.
Thus, the difference in each hour between two clocks will be, as follows:
$61-59=2\text{ minutes}$
Next, between 9:00 a.m. to 10:00 p.m., the total time difference is 13 hours.
So there will be a 2 minutes difference in 1 hour. Now, applying the unitary method, we get
For 13 hours, the difference should be: $13\times 2=26\text{ minutes}$
Hence, there should be a 26 minutes difference between the two clocks at 10:00 p.m. on the same day. Hence, the correct answer is option D.

Note: We have to be careful that for every one minute gain in one hour, we add 1 minute to 60 minutes. Also, for every 1 minute loose in one hour, we subtract 1 from 60 minutes.