Exactly how many minutes is it before seven o'clock, if 40 minutes ago it was three times as many minutes past two o'clock?

Puzzle Copyright © Kevin Stone

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Hint

How many minutes are there between 2:00 and 7:00?

Answer

65 minutes.

Reasoning

We need to break down the five hours in the following way:

3 x Answer minutes past two o'clock
40 minutes
Answer minutes before seven o'clock

Why? It is now Answer minutes before seven o'clock, and then we have the 40 minutes before that, and the remaining time was 3 x Answer minutes past two o'clock.

So, five hours = 5 x 60 = 300 minutes. We already know about the 40 minutes, so we have to share the remaining 260 minutes in the ratio 3:1, which gives 195:65 minutes. Or using algebra 4 x Answer = 300 - 40, so Answer = 65 minutes.

Therefore, the five hours is made up of:

195 minutes past two o'clock
40 minutes
65 minutes before seven o'clock

So, it's currently 65 minutes before 7:00 = 5:55.

Double-Checking

It is now 65 minutes before seven o'clock = 5:55, so 40 minutes ago it was 5:15 – which is 195 minutes after 2:00, as required (as 65 x 3 = 195).