Let user change posts per page

This is may not be the best solution, but it works. Following code needs to be added in functions.php.

add_filter('query_vars', 'parameter_queryvars' ); // Let WP accept the query argument we will use
function parameter_queryvars( $qvars )
{
    $qvars[] = 'posts_per_page';
    return $qvars;
}
add_action( 'pre_get_posts', 'change_post_per_page' ); // Filter posts based on passed query variable if set
function change_post_per_page( $query ) {
    global $wp_query;
    if ( !empty($wp_query->query['posts_per_page']) && is_numeric($wp_query->query['posts_per_page'])) {
        $query->set( 'posts_per_page', $wp_query->query['posts_per_page'] );
    }
}

To print the paging, (may require changes as per your scenario)

<div class="paging-per-post">
        <a href="http://<?php echo $_SERVER["HTTP_HOST"] . array_shift(explode('?',$_SERVER["REQUEST_URI"])) ?>?posts_per_page=15">15</a>
        <a href="http://<?php echo $_SERVER["HTTP_HOST"] . array_shift(explode('?',$_SERVER["REQUEST_URI"])) ?>?posts_per_page=30">30</a>
        <a href="http://<?php echo $_SERVER["HTTP_HOST"] . array_shift(explode('?',$_SERVER["REQUEST_URI"])) ?>?posts_per_page=50">50</a>
</div>