# Simple Puzzle: A Matter Of Time

I am trying to solve a simple puzzle:

Fifty Minutes ago if it was four times as many minutes past three O'clock, how many minutes is it to six O'clock.

I tried solving it:

Let x be the minutes past 5, then 120 + x - 50 = 4x

The correct solution has the formulation 180 - 50 -x = 4x which gives x = 26 and is the correct answer.

Am I doing weird thing by assuming that x is the minutes past 5 ? My approach is same as the one with correct solution if I use 4(60 -x) on the LHS but why should I ?

Is it that the puzzle is wrong in its formulation or am I missing something and hence am unable to arrive at the correct solution ?

By the way, the puzzle is from a famous book by Shakuntala Devi and hence I am forced to doubt the validity of my approach.

Because the time until $6$ is not the same as the time past $5$, treating $x$ this way results in a solution that is based on a false assumption. To remedy this, you would want to re-write the RHS to match with how you have written the LHS.

In order to avoid algebraic acrobatics, consider the problem as such: the "goal" time is $6$, which is $180$ minutes after $3$, but it is presently $x$ minutes prior to $6$. This gives us the $180-x$. Then we have that $50$ minutes ago, it was $4$ times longer after $3$ than it is presently before $6$, and this gives us the $-50$ and the $4x$.

Hence the book's set up is correct. The BIG problem is that the problem has a confusing wording. It would be easier to say: "If the time 50 minutes ago was 4 times as many minutes past three as the time now is before six, then what time is it now?"

• Yes, but suppose I get this question in an exam, then wouldn't the assumption that the question is talking about x as minutes past 5 more natural than minutes to 6 ? – adrian008 Jul 15 '15 at 22:34
• And I guess the only puzzling thing in the puzzle was the making the correct assumption of what x would be defined as ? – adrian008 Jul 15 '15 at 22:36
• Yes. The most puzzling part was understanding the question. As to the exam issue, the set up would just mean being certain to deal with the "minutes past 5" in a way that is equivalent to dealing with "minutes before 6". The only "natural" way to handle it is by using your native customs to tell the time, so I guess you are correct. – Terra Hyde Jul 15 '15 at 23:15

The problem (it appeared here already before, but without the strange "if") is worded in a completely misleading way. Maybe a mathematical moron from the assessment industry had it translated by Babelfish from a japanese or chinese source.

The sentence "Fifty minutes ago [if] it was four times as many minutes past three o'clock" can only be interpreted as "Fifty Minutes ago it was four times as many minutes past three o'clock than it is now" because no other point of comparison is given. If it is now $x$ minutes past three o'clock this means that $$720+x-50=4x\ ,$$ or $x=3{\rm h}\>43'\>20''$. It follows that it takes another $$11{\rm h}\>16'\>40''$$ until six o'clock.