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I came across a question in an ICAS exercise booklet for primary school in Australia. Ihe question is as follows:

At midnight on Friday, Megan's clock showed the correct time as 0:00 am.

At midnight on Saturday, her clock showed the time as 11:48 pm.

At midnight on Sunday, her clock showed the time as 11:36 pm.

At 6.00 am on Monday, Megan set her clock so that it showed 6:02 am.

What is the time difference, in minutes, between Megan's clock and the correct time of midnight on Thrusday the same week?

I calcuated the result as 43 minutes, but the key says it is 45 minutes. I'm not sure whether I've done it wrong or the key isn't right, or both. Please help me solve this problem. Thank you very much in advance.

Michael May
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You are correct.

Assuming that the clock loses $12$ minutes in $24$ hours, from $6\text{ am}$ on Monday to $12\text{ midnight}$ on Thursday, the clock would have lagged by $\frac{12}{24}(18+24\times3)-2=43$ minutes, considering that Megan set it $2$ minutes ahead initially.

Edit: As pointed out in the comments by Doug M, If you count the end of Wednesday as Thursday's midnight (i.e. day begins at 00:00 hrs), you would have $24$ less hours in the sum above, giving a lag of $43-12=31$ minutes.

Shubham Johri
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    Thursday at midnight is only 66 hours following 6 AM on Monday. The day begins at 00:00. – Doug M Jul 04 '20 at 03:36
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    @DougM Edited it. – Shubham Johri Jul 04 '20 at 03:41
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    I think the first way you did it conforms to common understanding of what "midnight means." Think about what you understand when someone says "midnight tonight" or "midnight tomorrow". – saulspatz Jul 04 '20 at 03:45
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    Yeah I retained it because at any rate, the question probably wanted us to use that convention... – Shubham Johri Jul 04 '20 at 03:46
  • Thank you, @ShubhamJohri, for your solution with analysis and calculation. It's really confusing when we consider Thusday midnight differently. – Michael May Jul 04 '20 at 04:26
  • Thank you, @saulspatz, for your discussion. I wonder whether there is a universally recognized convention for interpreting the concept of "midnight". Imagine what if a criminal case has to be described which happened at midnight of a certain day. – Michael May Jul 04 '20 at 04:29
  • However you interpret midnight, the key, which says $45$ minutes, is clearly wrong. – Gerry Myerson Jul 04 '20 at 06:50