I'm using a template where there is no link to 'older posts' at the bottom so as number of posts are increasing previous posts are disappearing from the main page without any link to them on the main page. I have set 10 posts/page option but it's showing just 3-4 posts.
Probably your theme uses a custom loop to display the posts on the homepage. Go to yoursiteurl.com/wp-admin/options-reading.php and see if Front page displays is set to Your latest posts or A static page . If Your latest posts is set, your theme should use a home.php, front-page.php or a index.php page as your homepage. If A static page is set, your theme is using a custom template file. Post here the option set.
Good, now look for a home.php or front-page.php inside the root of your current theme. If you can't find none of this file, open index.php and copy and paste the code here.
If your theme has a home.php or front-page.php file inside, copy and paste the code from those files. If not, copy and paste the code from index.php file.
Its happened due to your chosen theme which does not support or dont have space to have 10 post in home page. http://www.bestsoftinc.com/