$1$ man can eat $1$ apple in $1$ day.How many apples can six men eat in six days? $1$ man can eat $1$ apple in $1$ day.How many apples can six men eat in six days?

My approach:

$1$ men can eat $1$ apple in $1$ day.

Now, 6 men can eat in 6 days 6 apples only assuming each men eat $1$ apple a day.

Am I right in my approach?
no. 1 man can eat 1 apple in 1 day therefor 1 man can eat 6 apples in 6 days. therefor 6 men can eat 36 apples in 6 days....
The following piece by Lewis Carroll first appeared in ``The Monthly
Packet'' of February 1880 and is reprinted in _The_Magic_of_Lewis_Carroll_,
edited by John Fisher, Bramhall House, 1973.

                             Cats and Rats


If 6 cats kill 6 rats in 6 minutes, how many will be needed to kill 100
   rats in 50 minutes?

This is a good example of a phenomenon that often occurs in working
   problems in double proportion; the answer looks all right at first, but,
   when we come to test it, we find that, owing to peculiar circumstances in
   the case, the solution is either impossible or else indefinite, and needing
   further data.  The 'peculiar circumstance' here is that fractional cats or
   rats are excluded from consideration, and in consequence of this the
   solution is, as we shall see, indefinite.

The solution, by the ordinary rules of Double Proportion, is as follows:

   6 rats   :  100 rats  \
                          &gt;   :: 6 cats : ans.
  50 min.   :    6 min.  /

Then:  ans = (100)(6)(6)/(50)(6) = 12


But when we come to trace the history of this sanguinary scene through all
   its horrid details, we find that at the end of 48 minutes 96 rats are dead,
   and that there remain 4 live rats and 2 minutes to kill them in: the
   question is, can this be done?

Now there are at least four different ways in which the original feat,
   of 6 cats killing 6 rats in 6 minutes, may be achieved.  For the sake of
   clearness let us tabulate them:
      A.  All 6 cats are needed to kill a rat; and this they do in one minute,
          the other rats standing meekly by, waiting for their turn.
      B.  3 cats are needed to kill a rat, and they do it in 2 minutes.
      C.  2 cats are needed, and do it in 3 minutes.
      D.  Each cat kills a rat all by itself, and take 6 minutes to do it.

In cases A and B it is clear that the 12 cats (who are assumed to come
   quite fresh from their 48 minutes of slaughter) can finish the affair in
   the required time; but, in case C, it can only be done by supposing that 2
   cats could kill two-thirds of a rat in 2 minutes; and in case D, by
   supposing that a cat could kill one-third of a rat in two minutes.  Neither
   supposition is warranted by the data; nor could the fractional rats (even
   if endowed with equal vitality) be fairly assigned to the different cats.
   For my part, if I were a cat in case D, and did not find my claws in good
   working order, I should certainly prefer to have my one-third-rat cut off
   from the tail end.

In cases C and D, then, it is clear that we must provide extra cat-power.
   In case C less than 2 extra cats would be of no use.  If 2 were supplied,
   and if they began killing their 4 rats at the beginning of the time, they
   would finish them in 12 minutes, and have 36 minutes to spare, during which
   they might weep, like Alexander, because there were not 12 more rats to
   kill.  In case D, one extra cat would suffice; it would kill its 4 rats in
   24 minutes, and have 24 minutes to spare, during which it could have killed
   another 4.  But in neither case could any use be made of the last 2
   minutes, except to half-kill rats---a barbarity we need not take into
   consideration.

To sum up our results.  If the 6 cats kill the 6 rats by method A or B,
   the answer is 12; if by method C, 14; if by method D, 13.

This, then, is an instance of a solution made indefinite by the
   circumstances of the case. If an instance of the impossible be desired,
   take the following: If a cat can kill a rat in a minute, how many would be
   needed to kill it in the thousandth part of a second?  The mathematical
   answer, of course, is 60,000, and no doubt less than this would not
   suffice; but would 60,000 suffice?  I doubt it very much.  I fancy that at
   least 50,000 of the cats would never even see the rat, or have any idea of
   what was going on.

Or take this: `If a cat can kill a rat in a minute, how long would it be
   killing 60,000 rats?'  Ah, how long, indeed!  My private opinion is that
   the rats would kill the cat.