If two typists can type two pages in two minutes how many typists will it take to type 18 pages?

Answer 1

If two typists can type two pages in two minutes, then each one can type one page in two minutes, so he can type half page in a minute.

A typist that can type half page in a minute can type ,in 6 minutes, (0.5 * 6) pages, or 3 pages per minute; but we need 18 pages, so we need (18/3) typists, or 6 typists.

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As there is no time limit specified for typing the 18 pages, any number of typists can be used - the number of typists will affect the total time to type the 18 pages. (If no typists are used, then the pages will not get typed, so it can be assumed that at least one typist is being used).

For the shortest time to type the pages, the 18 pages are distributed as evenly as possible between the typists available and it is assumed that one page can only be typed by one typist::

If more than 18 typists are used, some will be sitting idle and not typing any pages.

If 18 typist are used, each will type one page.

If less than 18 are used, some (or all) will have to type more than 1 page.

The time taken for all the 18 pages to be typed will be the time for the typist(s) with the most number of pages to type their pages which is 2 minutes times the number of pages they have to type:

18+ typists → 2 minutes

9-17 typists → 4 minutes

6-8 typists → 6 minutes

5 typists → 8 minutes

4 typists → 10 minutes

3 typists → 12 minutes

2 typists → 18 minutes

1 typist → 36 minutes

Of course, the above assumes that the two pages of the question is the total number of pages typed, and not the number of pages each typist can type in two minutes which is a reasonable assumption based on the imprecise English used; to be precise either ..."can type two pages between them in ..." or "..can type two pages each in..." should be used.