Thanks. This helped.
I’m using a different template (Revolution Lifestyle), and there was no category.php file, just an archive.php file which controls the category pages.
When I tried copying the index.php to the archive.php, I got an error message, but then I went back and added the code you gave:
<?php
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
query_posts($query_string . '&showposts=10&paged=' . $paged);
?>
to appear before
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
which is what this template shows instead of
<?php if (have_posts()) : ?>
and this corrected the problem.