How to select and add the values if multiiple items in a checked list box?

Since an 'ItemCheck Event is always (well, it should be: see note below) followed by a ValueChanged Event (yes, that doesn't make a lot of sense, but that's the way it is), you can do this to make sure your 'sum calculation is always current.

This example assumes you have a multi-line TextBox on a Form, 'textBox1, and a CheckedListBox, 'checkedListBox1:

// flag to determine a change in CheckState of any Item
private bool IsCheckedChanged = false;

private void checkedListBox1_ItemCheck(object sender, ItemCheckEventArgs e)
{
    IsCheckedChanged = true;

    // for debugging only
    textBox1.Text += "change in Item CheckState" + Environment.NewLine;
}

private void checkedListBox1_SelectedIndexChanged(object sender, EventArgs e)
{
    // for debugging only
    textBox1.Text += "index changed" + Environment.NewLine + Environment.NewLine;
}

private void checkedListBox1_SelectedValueChanged(object sender, EventArgs e)
{
    // for debugging only
    textBox1.Text += "value changed" + Environment.NewLine;

    if (IsCheckedChanged)
    {
        int sum = 0;

        foreach (var chkItem in checkedListBox1.CheckedItems)
        {
            sum += Convert.ToInt32(chkItem);
        }

        // for debugging only
        textBox1.Text += "Sum: " + sum.ToString() + Environment.NewLine;

        IsCheckedChanged = false;
    }
}

If click Items rapidly in the CheckedListBox, and examine the content written to the TextBox, you will probably observe some instances where there is an irregularity in the way the various Events are fired. Yep, the Control ain't perfect !

But, most of the time a change in any Item's CheckState will trigger a ValueChanged Event, and you can evaluate the state of all CheckedItems reliably.

In using the native Windows Controls (or third-party Controls !), I strongly suggest you experiment with writing simple EventHandlers for the Events you are interested in that write some meaningful output to the Console or to a TextBox. Learning, and understanding, the order of execution, and inter-dependencies of the Events, is, imho, the only way to really be sure you understand how to use the given Control efficiently, and without creating subtle errors that are hard to understand/debug.

Why are you using SelectedItem property while you iterating CheckedItems?? This will work:

int sum = 0;
foreach (object item in checkedListBox1.CheckedItems)
{
    sum += Int32.Parse(item.ToString());
}

Thank You every one for your valuable time and solution but i have tried all the solution yet i get an exception saying "Input was not in a correct format when i tick the check box.