The Android One smartphones use the messaging app developed by Google. So, certain features may not be as evolved as you find in 3rd party text/SMS applications or on phones sold by other OEMs. Let's see if I can help you here:
Enable SMS Delivery Reports:
I am using Google's Android Messaging app, which I believe is the one shipped with the Android One smartphones. If not, the setup might differ slightly:
- Open Messages.
- Go to settings by tapping the 3 dots at the top right and choosing Settings.
- Tap on advanced and enable the toggle next to "Get SMS delivery reports".
Now compose a new SMS and send it to one of your contacts. A toast notification should appear at the bottom of the screen when the text gets delivered to the recipient.
Manually check for delivery report
Simply open the contact's chat window and tap on the text message. Please note that you just need to make a single tap and not tap and hold. When you do this, the field should expand a bit and show you the delivery details.