There is one app known as WhatsTools which can be downloaded from the play store and can be used for sending the large files.
After installing it you have to run this app and it will give a menu item as 'Turn on Service'.
Click or tap it to start.
Now Select Settings -->Accessibility -->WhatsTools Service.
Toggle it to 'On'.
It will give option of Google Drive and will ask you to 'sign in' in Google Drive.
Now sign in with your Google account (If you do not have then make one Google account).
Click or tap on the + sign.
It will display type of files like audio, video etc. Select the type you want to send.
It will now display files. Select the file you want to send.
Now click or tap on the Share menu.
Select WhatsApp in the next menu.
Now Select the WhatsApp contact of the recipient you want to share the file with and tap on Send.
The file will be uploaded to Google Drive and a link will be send to the recipient.
The recipient will click the link and get the file downloaded to his mobile.
This method can also be used to send the file to other applications like Facebook, Hike, Gmail etc.
Knowledge is power.