Shut down decision

Lauda Co has two divisions with the following results in the table below:
Division A Division B

————————————-Division A——Division B
—————————————–$m————–$m
Sales revenue——————–1000————1240
Variable costs———————400————–500
Contribution———————–600————–740
Divisional fixed costs————650————-600
Allocated Head Office costs—-50————-150
Divisional net loss—————(100)————(10)

If a division is shut down, then Lauda Co will avoid all the division’s specific costs and half of the Head Office costs allocated to the division.

What will be the revised total divisional net loss if Lauda Co chooses to shut down Division A?

The given answer is $35m
And they’ve used this approach :
Overall savings if A closed down = $75m
Current total divisional loss = ($110m)
Revised total divisional loss : ($110m) + $75m = $35m

But, I followed this, after finding net savings of $75m of closing A,
Now that Division A is closed :

Division B net loss is : ($10m)
Allocated HO cost $25m is still incurred after closing A so : ($25m)
And finally the savings of the closure : $75m
Revised profit :
-10 -25 +75 = $40m profit, not $35m loss.

Sir, please help me out