How to execute a sudo script with double click

I have this script to shutdown my system after 30 seconds. I want to run this script by double clicking it (that option I changed in nautilus). This is the content of my script

#!/bin/bash
shutdown -h +30;
echo "succesfull"
read -p "Press any key to continue... " -n1 -s

to make sudo script executable without a password I followed this answer and I am able to execute this script from the terminal without using a password (sudo ~/test/test.sh). The problem is when I double click the above script it's again asking for root privileges:

shutdown: Need to be root
successful
Press any key to continue... 

What's the problem here?

You can make a conditional to relaunch the script as root if it's launched as a normal user.

To shutdown the computer:

#!/bin/bash

if [[ $USER == "eka" ]]; then       # If the script is ran as "eka" then...
    sudo $0                         # relaunch it as "root".
    exit 0                          # Once it finishes, exit gracefully.
elif [[ $USER != "root" ]]; then    # If the user is not "eka" nor "root" then...
    exit 0                          # Once it finishes, exit gracefully.
fi                                  # End if.

shutdown -h +30;
read -p "Press any key to continue... " -n1 -s

Simplified version:

#!/bin/bash

[[ $USER == "eka" ]] && { sudo $0; exit 0; }
[[ $USER != "root" ]] && exit 0

shutdown -h +30;

Very simplified version (not recommended):

#!/bin/bash

sudo $0          # Relaunch script as root (even if it's already running as root)
shutdown -h +30; # Shutdown the computer in 30 seconds.

To suspend the computer:

#!/bin/bash

if [[ $USER == "eka" ]]; then                 # If the script is ran as "eka":
    gnome-screensaver-command -a                  # Lock computer.
else                                          # Else:
    sudo -u eka gnome-screensaver-command -a      # Once it finishes, exit gracefully.
fi                                            # End if.

Simplified version:

#!/bin/bash

[[ $USER != "eka" ]] && { sudo -u eka gnome-screensaver-command -a; exit 0; }

Very simplified version:

#!/bin/bash

sudo -u eka gnome-screensaver-command -a

Note: $0 is a variable that holds the full path to the script.